Talk_id  Date  Speaker  Title 
17497

Monday 1/7 4:10 PM

Matthew Ballard, University of South Carolina

Exceptional collections: what they are and where to find them (special colloquium)
 Matthew Ballard, University of South Carolina
 Exceptional collections: what they are and where to find them (special colloquium)
 01/07/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
Analogous to orthonormal bases in linear algebra, exceptional collections in triangulated categories are the most atomic means of decomposition. In this talk, we will introduce exceptional collections drawing heavily on examples from noncommutative algebra, algebraic geometry and symplectic geometry. We will then address the question of where (and how) to find them.

17495

Wednesday 1/9 4:10 PM

Eugenia Malinnikova, Norwegian University of Science and Technology

Quantitative unique continuation for elliptic PDEs and application (special colloquium)
 Eugenia Malinnikova, Norwegian University of Science and Technology
 Quantitative unique continuation for elliptic PDEs and application (special colloquium)
 01/09/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
If a solution to a uniformly elliptic second order PDE with smooth coefficients vanishes on an open subset of a domain then it is zero on the whole domain. This is a classical result known as weak unique continuation. We will discuss stronger versions, including some recent quantitative results and outline applications to the study of eigenfunctions of LaplaceBeltrami operator on compact manifolds.

17501

Friday 1/11 4:10 PM

Pavlo Pylyavskyy, University of Minnesota

Zamolodchikov periodicity and integrability (special colloquium)
 Pavlo Pylyavskyy, University of Minnesota
 Zamolodchikov periodicity and integrability (special colloquium)
 01/11/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
Tsystems are certain discrete dynamical systems associated with quivers. They appear in several different contexts: quantum affine algebras and Yangians, commuting transfer matrices of vertex models, character theory of quantum groups, analytic Bethe ansatz, WronskianCasoratian duality in ODE, gauge/string theories, etc. Periodicity of certain Tsystems was the main conjecture in the area until it was proven by Keller in 2013 using cluster categories. In this work we completely classify periodic Tsystems, which turn out to consist of 5 infinite families and 4 exceptional cases, only one of the infinite families being known previously. We then proceed to classify Tsystems that exhibit two forms of integrability: linearization and zero algebraic entropy. All three classifications rely on reduction of the problem to study of commuting Cartan matrices, either of finite or affine types. The finite type classification was obtained by Stembridge in his study of KazhdanLusztig theory for dihedral groups, the other two classifications are new. This is joint work with Pavel Galashin.

17500

Monday 1/14 4:10 PM

Alex Blumenthal, University of Maryland

Chaotic regimes for random dynamical systems (special colloquium)
 Alex Blumenthal, University of Maryland
 Chaotic regimes for random dynamical systems (special colloquium)
 01/14/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
It is anticipated that chaotic regimes (characterized by, e.g., sensitivity with respect to initial conditions and loss of memory) arise in a wide variety of dynamical systems, including those arising from the study of ensembles of gas particles and fluid mechanics. However, in most cases the problem of rigorously verifying asymptotic chaotic regimes is notoriously difficult. For volumepreserving systems (e.g., incompressible fluid flow or Hamiltonian systems), these issues are exemplified by coexistence phenomena: even in quite simple models which should be chaotic, e.g. the Chirikov standard map, completely opposite dynamical regimes (elliptic islands vs. hyperbolic sets) can be tangled together in phase space in a convoluted way.
Recent developments have indicated, however, that verifying chaos is tractable for systems subjected to a small amount of noise— from the perspective of modeling, this is not so unnatural, as the real world is inherently noisy. In this talk, I will discuss two recent results: (1) a large positive Lyapunov exponent for (extremely small) random perturbations of the Chirikov standard map, and (2) a positive Lyapunov exponent for the Lagrangian flow corresponding to various incompressible stochastic fluids models, including stochastic 2D NavierStokes and 3D hyperviscous NavierStokes on the periodic box. The work in this talk is joint with Jacob Bedrossian, Samuel PunshonSmith, Jinxin Xue and LaiSang Young.

17502

Wednesday 1/16 1:40 PM

Goncalo Oliveira, Universidade Federal Fluminense, Rio de Janeiro

Gauge theory on AloffWallach spaces
 Goncalo Oliveira, Universidade Federal Fluminense, Rio de Janeiro
 Gauge theory on AloffWallach spaces
 01/16/2019
 1:40 PM  3:00 PM
 C517 Wells Hall
I will describe joint work with Gavin Ball constructing and classifying G2instantons on AloffWallach spaces, which are the most interesting known examples of compact "nearlyparallel" G2manifolds.

15383

Thursday 1/17 2:00 PM

Chris Kottke, New College Florida

Compactification of monopole moduli spaces
 Chris Kottke, New College Florida
 Compactification of monopole moduli spaces
 01/17/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
I will discuss joint work with Michael Singer and Karsten Fritzsch on compactifications of the moduli spaces $M_k$ of $\mathrm{SU}(2)$ magnetic monopoles on $\mathbf{R}^3$ . Via a geometric gluing procedure, we construct manifolds with corners compactifying the $M_k$ , the boundaries of which represent monopoles of charge $k$ decomposing into widely separated ‘monopole clusters' of lower charge. The hyperkahler metric on $M_k$ has a complete asymptotic expansion, the leading terms of which generalize the asymptotic metric discovered by Bielawski, Gibbons and Manton in the case that the monopoles are all widely separated. From the structure of the compactification, we are able to make partial progress toward proving Sen's conjecture for $L^2$ cohomology of the moduli spaces.

17506

Thursday 1/17 3:00 PM

Daping Weng, MSU

More on Scattering Diagram and Theta Functions
 Daping Weng, MSU
 More on Scattering Diagram and Theta Functions
 01/17/2019
 3:00 PM  4:00 PM
 C117 Wells Hall
I will continue the discussion on scattering diagram and theta functions and relate them to the classical cluster theories. I will sketch GrossHackingKeelKontsevich’s proofs of positive Laurent phenomenon, sign coherence, and a weak version of the cluster duality conjecture.

17503

Monday 1/21 1:40 PM

Zhe Zhang, MSU

Harmonic map flow in dimension two, I
 Zhe Zhang, MSU
 Harmonic map flow in dimension two, I
 01/21/2019
 1:40 PM  3:00 PM
 C517 Wells Hall
Bubbling analysis due to Struwe.

17496

Monday 1/21 4:10 PM

Wencai Liu, University of California, Irvine

Universal arithmetical hierarchy of eigenfunctions for supercritical almost Mathieu operators (special colloquium)
 Wencai Liu, University of California, Irvine
 Universal arithmetical hierarchy of eigenfunctions for supercritical almost Mathieu operators (special colloquium)
 01/21/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
The Harper's model is a tightbinding description of Bloch electrons on $\mathbb{Z}^2$ under a constant transverse magnetic field.
In 1964, Mark Azbel predicted that both spectra and eigenfunctions of this model
have selfsimilar hierarchical structure driven by the continued fraction expansion of the irrational magnetic flux.
In 1976, the hierarchical structure of spectra was discovered numerically by Douglas Hofstadter, and was later observed in various experiments. The mathematical study of Harper's model led to the development of spectral theory of the almost Mathieu operator, with the solution of the Ten Martini Problem partially confirming the fractal structure of the spectrum.
In this talk we will present necessary background and discuss the main ideas behind our confirmation (joint with S. Jitomirskaya) of Azbel's second prediction of the structure of the eigenfunctions. More precisely, we show that the eigenfunctions of the almost Mathieu operators in the localization regime, feature selfsimilarity governed by the continued fraction expansion of the frequency. These results also lead to the proof of sharp arithmetic transitions between pure point and singular continuous spectra, both in the frequency and the phase, as conjectured in 1994.

17511

Wednesday 1/23 10:20 AM

Stavros Garoufalidis, Georgia Institute of Technology

A brief history of quantum topology (special colloquium)
 Stavros Garoufalidis, Georgia Institute of Technology
 A brief history of quantum topology (special colloquium)
 01/23/2019
 10:20 AM  11:10 AM
 C304 Wells Hall
Quantum topology originated from Vaughan Jones's discovery of the Jones polynomial of a knot in 1985. I will explain the area and its interaction with mathematical physics, algebra, analysis, number theory and combinatorics.

16468

Thursday 1/24 2:00 PM

Rebecca Winarski, University of Michigan

Solving the Twisted Rabbit Problem using trees
 Rebecca Winarski, University of Michigan
 Solving the Twisted Rabbit Problem using trees
 01/24/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
The twisted rabbit problem is a celebrated problem in complex dynamics. Work of Thurston proves that up to equivalence, there are exactly three branched coverings of the sphere to itself satisfying certain conditions. When one of these branched coverings is modified by a mapping class, a map equivalent to one of the three coverings results. Which one?
After remaining open for 25 years, this problem was solved by BartholdiNekyrashevych using iterated monodromy groups. In joint work with Belk, Lanier, and Margalit, we present an alternate solution using topology and geometric group theory that allows us to solve a more general problem.

17512

Thursday 1/24 3:00 PM

Daping Weng, MSU

More on Scattering Diagram and Theta Functions
 Daping Weng, MSU
 More on Scattering Diagram and Theta Functions
 01/24/2019
 3:00 PM  4:00 PM
 C204A Wells Hall
I will continue the discussion on scattering diagram and theta functions and relate them to the classical cluster theories. I will sketch GrossHackingKeelKontsevich’s proofs of positive Laurent phenomenon, sign coherence, and a weak version of the cluster duality conjecture.

17504

Monday 1/28 1:40 PM

Zhe Zhang, MSU

Harmonic map flow in dimension two, II
 Zhe Zhang, MSU
 Harmonic map flow in dimension two, II
 01/28/2019
 1:40 PM  3:00 PM
 C517 Wells Hall
Bubble tree analysis and energy identity.

17526

Monday 1/28 3:00 PM

Nick Ovenhouse, MSU

Total Positivity
 Nick Ovenhouse, MSU
 Total Positivity
 01/28/2019
 3:00 PM  4:00 PM
 C517 Wells Hall
A matrix is "totally positive" if all of its minors are positive. We will discuss combinatorial models of total positivity using weighted graphs, as well as some criteria and characterizations for checking total positivity. If there is time, we will also discuss total positivity in the Grassmannian manifold, along with combinatorial models.

17529

Wednesday 2/6 1:40 PM

Tom Parker, MSU

Convergence modulo diffeomorphisms of maps from Riemann surfaces
 Tom Parker, MSU
 Convergence modulo diffeomorphisms of maps from Riemann surfaces
 02/06/2019
 1:40 PM  3:00 PM
 C517 Wells Hall
For the theory of both harmonic and holomorphic maps, one needs a notion of convergence maps modulo diffeomorphisms of the domain. I will describe an approach (developed with Woongbae Park) that uses Kuranishi families in place of the standard approach based on bubble tree convergence.

17515

Wednesday 2/6 4:10 PM

Abhishek Mallick

Computations in equivariant Floer homology
 Abhishek Mallick
 Computations in equivariant Floer homology
 02/06/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
Following HendricksLipshitz Sarkar we discuss the construction of equivariant Floer homology and a few cases where it can be computed.

16478

Wednesday 2/6 4:10 PM

Mihai Tohaneanu, University of Kentucky

Local energy estimates on black hole backgrounds
 Mihai Tohaneanu, University of Kentucky
 Local energy estimates on black hole backgrounds
 02/06/2019
 4:10 PM  5:00 PM
 C517 Wells Hall
Local energy estimates are a robust way to measure decay of solutions to linear wave equations. I will discuss several such results on black hole backgrounds, such as Schwarzschild, Kerr, and suitable perturbations converging at various rates, and briefly discuss applications to nonlinear problems. The most challenging geometric feature one needs to deal with is the presence of trapped null geodesics, whose presence yield unavoidable losses in the estimates. This is joint work with Lindblad, Marzuola, Metcalfe, and Tataru.

15394

Thursday 2/7 2:00 PM

Adam Sikora, SUNY at Buffalo

New Approach to Quantum Teichmuller Theory
 Adam Sikora, SUNY at Buffalo
 New Approach to Quantum Teichmuller Theory
 02/07/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
The Jones polynomial invariant of links in R^3 extends to links in thickened surfaces, leading to the notion of the skein algebra of a surface, which is a version of ChekhovFock quantum Teichmuller space. The algebraic structure of skein algebras is quite rich and mysterious. We will approach it using the theory of measured foliations and pseudoAnosov diffeomorphisms of surfaces

17527

Thursday 2/7 3:00 PM

Elizabeth Munch, MSU

The Interleaving Distance for a Category with a Flow
 Elizabeth Munch, MSU
 The Interleaving Distance for a Category with a Flow
 02/07/2019
 3:00 PM  3:50 PM
 C304 Wells Hall
All data has noise, and rigorously understanding how your analysis fares in the face of that noise requires a notion of a metric. The idea of the interleaving distance arose in the context of generalizing metrics for persistence modules from the field of topological data analysis (TDA). Essentially, the idea is that two objects in a category should be distance 0 if there is an isomorphism between them; the distance between two objects should be "almost" 0 if there is "almost" an isomorphism between them. Placed in the right context, we can measure what we mean by an "almost'' isomorphism and use this to define a distance.
Building on the work of Chazal et al.; and Bubenick, Scott, and de Silva, we will discuss the generalization of the notion of the interleaving distance to a socalled "category with a flow". We will show that this generalization provides metrics for many different categories of interest in TDA and beyond, including Reeb graphs, merge trees, phylogenetic trees, and mapper graphs. This work is the result of collaborations with Anastasios Stefanou, Vin de Silva, and Amit Patel.

17528

Thursday 2/7 3:00 PM

Alek Vainshtein, University of Haifa

Exotic cluster structures on SL_n
 Alek Vainshtein, University of Haifa
 Exotic cluster structures on SL_n
 02/07/2019
 3:00 PM  4:00 PM
 C204A Wells Hall
Back in 2005, Berenstein, Fomin and Zelevinsky discovered a cluster
structure in the ring of regular functions on a double Bruhat cell in a
semisimple Lie group, in particular, SL_n. This structure can be easily
extended to the whole group. The compatible Poisson bracket is given by
the standard rmatrix PoissonLie structure on SL_n. The latter is a
particular case of PoissonLie structures corresponding to
quasitriangular Lie bialgebras. Such structures where classified in
1982 by Belavin and Drinfeld. In 2012, we have conjectured that each
PoissonLie structure on SL_n gives rise to a cluster structure, and
gave several examples of exotic cluster structures corresponding to
PoissonLie structures distinct from the standard one. In my talk I will
tell about the progress in the proof of this conjecture and its
modifications.
Joint with M.Gekhtman and M.Shapiro.

17530

Monday 2/11 1:40 PM

Xiaodong Wang, MSU

Harmonic maps and superrigidity (after MokSiuYeung)
 Xiaodong Wang, MSU
 Harmonic maps and superrigidity (after MokSiuYeung)
 02/11/2019
 1:40 PM  3:00 PM
 C517 Wells Hall
No abstract available.

17513

Monday 2/11 4:10 PM

Cori FataHartley and Cheryl Sisk

Designation B Process
 Cori FataHartley and Cheryl Sisk
 Designation B Process
 02/11/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
Dr. FataHartley and Dr. Sisk will describe the Designation B requirements and application process. They will answer questions about eligibility, timeline, procedures, etc.

17490

Wednesday 2/13 4:10 PM

Albert Ai, UC Berkeley

Low Regularity Solutions for Gravity Water Waves
 Albert Ai, UC Berkeley
 Low Regularity Solutions for Gravity Water Waves
 02/13/2019
 4:10 PM  5:00 PM
 C517 Wells Hall
We consider the local wellposedness of the Cauchy problem for the gravity water waves equations, which model the free interface between a fluid and air in the presence of gravity. It has been known that by using dispersive effects, one can lower the regularity threshold for wellposedness, below that which is attainable by energy estimates alone. This program was initiated for gravity water waves by AlazardBurqZuily, by proving Strichartz estimates with loss. We discuss how these Strichartz estimates, and thus the low regularity threshold, can be sharpened by applying an integration along the Hamilton flow combined with local smoothing estimates.

17516

Wednesday 2/13 4:10 PM

Keshav Sutrave

Harmonic map heat flow
 Keshav Sutrave
 Harmonic map heat flow
 02/13/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
The harmonic map flow equation and EellsSampson theorem.

17499

Thursday 2/14 2:00 PM

Melissa Zhang, Boston College

Localization in Khovanov homology
 Melissa Zhang, Boston College
 Localization in Khovanov homology
 02/14/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
When a topological object admits a group action, we expect that our invariants reflect this symmetry in their structure. This talk will tour the expression of link symmetries in three generations of related invariants: the Jones polynomial; its categorification, Khovanov homology; and the youngest invariant in the family, the Khovanov stable homotopy type, introduced by Lipshitz and Sarkar. I will describe how to use LawsonLipshitzSarkar's Burnside functor construction of the LipshitzSarkar Khovanov homotopy type to produce localization theorems and Smithtype inequalities for the Khovanov homology of periodic links. This joint work with Matthew Stoffregen.

17507

Thursday 2/14 3:00 PM

Alexander Shapiro, The University of Edinburgh

Positive PeterWeyl theorem
 Alexander Shapiro, The University of Edinburgh
 Positive PeterWeyl theorem
 02/14/2019
 3:00 PM  4:00 PM
 C204A Wells Hall
The classical PeterWeyl theorem asserts that the regular representation of a compact Lie group $G$ on the space of squareintegrable functions $L^2(G)$ decomposes as the direct sum of all irreducible unitary representations of $G$. In the talk, I will use positive representations of cluster varieties, to obtain a "noncompact" quantum analogue of the PeterWeyl theorem. This is joint work with Ivan Ip and Gus Schrader.

17532

Friday 2/15 4:10 PM

Nicolas Garcia Trillos, University of WisconsinMadison

Large sample asymptotics of spectra of Laplacians and semilinear elliptic PDEs on random geometric graphs
 Nicolas Garcia Trillos, University of WisconsinMadison
 Large sample asymptotics of spectra of Laplacians and semilinear elliptic PDEs on random geometric graphs
 02/15/2019
 4:10 PM  5:00 PM
 1502 Engineering Building
Given a data set $\mathcal{X}=\{x_1, \dots, x_n\}$ and a weighted graph structure $\Gamma= (\mathcal{X},W)$ on $\mathcal{X}$, graph based methods for learning use analytical notions like graph Laplacians, graph cuts, and Sobolev seminorms to formulate optimization problems whose solutions serve as sensible approaches to machine learning tasks. When the data set consists of samples from a distribution supported on a manifold (or at least approximately so), and the weights depend inversely on the distance between the points, a natural question to study concerns the behavior of those optimization problems as the number of samples goes to infinity. In this talk I will focus on optimization problems closely connected to clustering and supervised regression that involve the graph Laplacian. For clustering, the spectrum of the graph Laplacian is the fundamental object used in the popular spectral clustering algorithm. For regression, the solution to a semilinear elliptic PDE on the graph provides the minimizer of an energy balancing regularization and data fidelity, a sensible object to use in nonparametric regression.
Using tools from optimal transport, calculus of variations, and analysis of PDEs, I will discuss a series of results establishing the asymptotic consistency (with rates of convergence) of many of these analytical objects, as well as provide some perspectives on future research directions.

17533

Friday 2/15 4:10 PM

Willie Wong, MSU

In the beginning ... : Big Bang and Bianchi IX
 Willie Wong, MSU
 In the beginning ... : Big Bang and Bianchi IX
 02/15/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
Big Bang Theory is now an established part of cosmology. A common mental picture of the big bang singularity is that of the Friedman model, where, looking backwards in time, the universe collapses uniformly to one point leaving the shape unchanged. In 1970, however, the Russian physicists Belinskii, Khalatnikov, and Lifshitz showed that the Friedmaninspired picture is far from common. In fact they proposed an alternative picture where near the beginning of time, the generic universe rapidly and chaotically oscillates between different "shapes" as it shrinks down to a single point. I aim to explain some of the things we now know about this BKL conjecture, including an interesting connection to the continued fraction expansion of real numbers and the golden ratio.

17531

Monday 2/18 1:40 PM

Leonardo Abbrescia, MSU

Moser iteration for parabolic equations
 Leonardo Abbrescia, MSU
 Moser iteration for parabolic equations
 02/18/2019
 1:40 PM  3:00 PM
 C517 Wells Hall
No abstract available.

17540

Monday 2/18 3:00 PM

Charlotte Ure, MSU

Prime Torsion of the Brauer Group of an Elliptic Curve
 Charlotte Ure, MSU
 Prime Torsion of the Brauer Group of an Elliptic Curve
 02/18/2019
 3:00 PM  4:00 PM
 C517 Wells Hall
The Brauer group is an invariant, that can detect arithmetic properties of the underlying variety. In this talk, I will define the Brauer group of a variety, describe it's connection to rational points, and give an algorithm to calculate generators and relations of the qtorsion of the Brauer group of and elliptic curve., where q is prime. This talk will be accessible to all.

17514

Tuesday 2/19 2:00 PM

Paul Dawkins, Northern Illinois University

The use(s) of “is” in Mathematics
 Paul Dawkins, Northern Illinois University
 The use(s) of “is” in Mathematics
 02/19/2019
 2:00 PM  3:30 PM
 252 EH
This talk presents analysis of some of the ambiguities that arise among statements with the copular verb “is" in the mathematical language of textbooks as compared to daytoday English language. We identify patterns in the construction and meaning of is statements using randomly selected examples from corpora representing the two linguistic registers. We categorize these examples according to the part of speech of the object word in the grammatical form “[subject] is [object].” In each such grammatical category, we compare the relative frequencies of the subcategories of logical relations conveyed by that construction. Within some categories we observe that the same grammatical structure alternatively conveys different logical relations and that the intended logical relation can only sometimes be inferred from the grammatical cues in the statement itself. This means that one can only interpret the intended logical relation by already knowing the relation among the semantic categories in question. Such ambiguity clearly poses a communicative challenge for teachers and students. We discuss the pedagogical significance of these patterns in mathematical language and consider the relationship between these patterns and mathematical practices.

17517

Wednesday 2/20 4:10 PM

Zhe Zhang

A construction of the DeligneMumford orbifold
 Zhe Zhang
 A construction of the DeligneMumford orbifold
 02/20/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
Isomorphism classes $M_{g,n}$ of stable nodal Riemann surfaces of arithmetic genus g with n marked points. A marked nodal Riemann surface is stable if and only if its isomorphism group is finite. A natural construction based on the existence of universal unfoldings endows the DeligneMumford moduli space with an orbifold structure. Here we use the methods of differential geometry rather than algebraic geometry.

17505

Thursday 2/21 2:00 PM

Ilya Gekhtman , University of Toronto

Growth rates of invariant random subgroups of hyperbolic groups and rank 1 Lie groups.
 Ilya Gekhtman , University of Toronto
 Growth rates of invariant random subgroups of hyperbolic groups and rank 1 Lie groups.
 02/21/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
Abstract: Invariant random subgroups (IRS) are conjugacy invariant probability measures on the space of subgroups of a given group G. They arise naturally as point stabilizers of probability measure preserving actions. The space of invariant random subgroups of SL_{2}R can be regarded as a natural compactification of the moduli space of Riemann surfaces, related to the DeligneMumford compactification. Invariant random subgroups can be regarded as a generalization both of normal subgroups and of lattices in topological groups. As such, it is interesting to extend results from the theories of normal subgroups and of lattices to the IRS setting.
Jointly with Arie Levit, we prove such a result: the critical exponent (exponential growth rate) of an infinite IRS in an isometry group of a Gromov hyperbolic space (such as a rank 1 Lie group, or a hyperbolic group) is almost surely greater than half the Hausdorff dimension of the boundary.
This generalizes an analogous result of MatsuzakiYabukiJaerisch for normal s
As a corollary, we obtain that if $\Gamma$ is a typical subgroup and $X$ a rank 1 symmetric space then $\lambda_{0}(X/\Gamma)<\lambda_{0}(X)$ where $\lambda_0$ is the bottom of the spectrum of the Laplacian. The proof uses ergodic theorems for actions of hyperbolic groups.
I will also talk about results about growth rates of normal subgroups of hyperbolic groups that inspired this work.

17539

Thursday 2/21 3:00 PM

Xiaochuan Yang, University of Luxembourg

BerryEsseen Bounds in the BreuerMajor Central Limit Theorem
 Xiaochuan Yang, University of Luxembourg
 BerryEsseen Bounds in the BreuerMajor Central Limit Theorem
 02/21/2019
 3:00 PM  3:50 PM
 C405 Wells Hall
The BreuerMajor theorem provides sufficient conditions in order that a normalized sum of nonlinear functionals of Gaussian random fields exhibits Gaussian fluctuation. Such a result has farreaching applications in statistical inference of Gaussian models. In this talk, I will be focusing on the rate of convergence in the total variation distance of the BreuerMajor theorem. To this end, we apply Malliavin calculus (stochastic calculus of variation) techniques, Stein’s method for normal approximations, and Gebelein’s inequality for functionals of correlated Gaussian fields. Based on joint work with I. Nourdin and G. Peccati.

17545

Monday 2/25 1:40 PM

Alex Waldron, MSU

Twisted harmonic maps and the selfduality equations
 Alex Waldron, MSU
 Twisted harmonic maps and the selfduality equations
 02/25/2019
 1:40 PM  2:50 PM
 C517 Wells Hall
I will describe Donaldson's 1986 paper with the same title.

17544

Monday 2/25 3:00 PM

Duff BakerJarvis, MSU

QSym and the Shuffle Compatibility of Permutation Statistics
 Duff BakerJarvis, MSU
 QSym and the Shuffle Compatibility of Permutation Statistics
 02/25/2019
 3:00 PM  4:00 PM
 C517 Wells Hall
The fundamental basis of the Hopf algebra of quasisymmetric functions can be thought of in terms of shuffling permutations, however we do not distinguish between permutations that have the same descent set. We can thus think of the algebra structure of QSym as having a basis indexed by equivalence classes of permutations. This descent set, Des, is a simple example of a permutation statistic that exhibits a property called being shuffle compatible. We will show that permutation statistics that are shuffle compatible give rise to “shuffle algebras” that are quotients of QSym and then discuss some bijective proofs that certain statistics are shuffle compatible.

17535

Monday 2/25 4:10 PM

Round Table Discussion

Pros and Cons for Evening Exams for Uniform Courses
 Round Table Discussion
 Pros and Cons for Evening Exams for Uniform Courses
 02/25/2019
 4:10 PM  5:00 PM
 C109 Wells Hall
No abstract available.

17518

Wednesday 2/27 4:10 PM

Woongbae Park

Analysis of measures converging to a Diracdelta measure in Riemann surfaces
 Woongbae Park
 Analysis of measures converging to a Diracdelta measure in Riemann surfaces
 02/27/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
This is a 2dim case of general energy concentration phenomenon. If we have sequence of harmonic maps with bounded energy defined on a Riemann surface, Uhlenbeck compactness theorem says its subsequence converges away from at most finite points, called bubble points. At the bubble point energy concentrates, so we may blow up the point to capture energy distribution on the bubble. But energy may concentrate again on the bubble, so careful touch is needed to finish this blow up process. In this talk I will introduce a way to choose two marked points with desired properties. The typical example is of harmonic map case, but it may be applied to other energy concentrating cases.

17509

Thursday 2/28 2:00 PM

Eva Belmont, Northwestern University

Localizing the E_2 page of the Adams spectral sequence
 Eva Belmont, Northwestern University
 Localizing the E_2 page of the Adams spectral sequence
 02/28/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
The Adams spectral sequence is one of the central tools for calculating the stable homotopy groups of spheres, one of the motivating problems in stable homotopy theory. This talk focuses on the E_2 page, which can be calculated algorithmically in a finite range but whose largescale structure is too complicated to be understood in full. I will give an introduction to some features of the Adams E_2 page for the sphere at p = 3, and discuss an approach for calculating it in an infinite region. This approach relies on computing an analogue of the Adams spectral sequence in Palmieri's stable category of comodules, which can be regarded as an algebraic analogue of stable homotopy theory.

17543

Thursday 2/28 3:00 PM

Linhui Shen, MSU

Cluster structure on moduli spaces of local systems for general groups
 Linhui Shen, MSU
 Cluster structure on moduli spaces of local systems for general groups
 02/28/2019
 3:00 PM  4:00 PM
 C204A Wells Hall
There have been several references in the literature devoted to the study of the cluster structures on moduli spaces of Glocal systems, all of which are based on case by case study. In this talk, we present a systematic construction that works for all groups at once. As an application, we will investigate the principal series representations of quantum groups from the perspective of cluster theory.

17548

Thursday 2/28 3:00 PM

Ikpe Dennis, MSU

A Levy RegimeSwitching Temperature Dynamics Model for Weather Derivatives
 Ikpe Dennis, MSU
 A Levy RegimeSwitching Temperature Dynamics Model for Weather Derivatives
 02/28/2019
 3:00 PM  3:50 PM
 C405 Wells Hall
Linked Abstract

17537

Thursday 3/7 2:00 PM

SPRING BREAK

SPRING BREAK
 SPRING BREAK
 SPRING BREAK
 03/07/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
No abstract available.

17554

Monday 3/11 1:40 PM

Gorapada Bera

Taubes' approach to the Casson invariant: an overview
 Gorapada Bera
 Taubes' approach to the Casson invariant: an overview
 03/11/2019
 1:40 PM  3:00 PM
 C304 Wells Hall
No abstract available.

17536

Monday 3/11 4:10 PM

Round Table Discussion

Poll Everywhere and other inclass participation technologies
 Round Table Discussion
 Poll Everywhere and other inclass participation technologies
 03/11/2019
 4:10 PM  5:00 PM
 C109 Wells Hall
No abstract available.

17553

Tuesday 3/12 3:00 PM

Huyi Hu, MSU

The essential coexistence phenomenon in Hamiltonian dynamics
 Huyi Hu, MSU
 The essential coexistence phenomenon in Hamiltonian dynamics
 03/12/2019
 3:00 PM  4:00 PM
 C304 Wells Hall
We construct an example of a Hamiltonian flow $f^t$ on a $4$dimensional smooth manifold $\mathcal{M}$ which after being restricted to an energy surface $\mathcal{M}_e$ demonstrates essential coexistence of regular and chaotic dynamics, that is, there is an open and dense $f^t$invariant subset $U\subset\mathcal{M}_e$ such that the restriction $f^tU$ has nonzero Lyapunov exponents in all directions (except the direction of the flow) and is a Bernoulli flow while on the boundary $\partial U$, which has positive volume, all Lyapunov exponents of the system are zero.
This is a continuation of the talk in previous week.

17547

Tuesday 3/12 4:00 PM

Kristen Hendricks, Michigan State University

Classical and Modern Invariants of Knots
 Kristen Hendricks, Michigan State University
 Classical and Modern Invariants of Knots
 03/12/2019
 4:00 PM  5:00 PM
 C304 Wells Hall
We'll give a brief introduction to what knot theory is and why you might want to study it, and talk about some classical invariants of knots and what they detect. We'll then introduce a modern invariant called Heegaard Floer knot homology from the early 2000s, and talk about its properties and its relationship to classical invariants. This talk should be accessible to undergraduate students.

17555

Wednesday 3/13 3:00 PM

Yusuf Mustopa, UMass Amherst/Tufts University

Effective Global Generation on Varieties with Numerically Trivial Canonical Bundle
 Yusuf Mustopa, UMass Amherst/Tufts University
 Effective Global Generation on Varieties with Numerically Trivial Canonical Bundle
 03/13/2019
 3:00 PM  4:00 PM
 C304 Wells Hall
Fujita’s freeness conjecture predicts that if X is a smooth projective variety and A is an ample divisor on X, then K+mA is basepointfree when m is at least dim(X)+1. Although this statement is optimal (as can be seen when X is projective space) there are much better statements for abelian varieties and surfaces with numerically trivial canonical bundle. In this talk, I will discuss a result of Fujita type for smooth projective varieties having numerically trivial canonical bundle, as well as its application to moduli spaces of sheaves on abelian surfaces. This is joint work with Alex Kuronya.

17520

Wednesday 3/13 4:10 PM

Hitesh Gakhar

Sliding window embeddings
 Hitesh Gakhar
 Sliding window embeddings
 03/13/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
Classically, Sliding Window Embeddings were used in the study of dynamical systems to reconstruct topology of underlying attractors from generic observation functions. In 2015, Perea and Harer studied persistent homology of sliding window embeddings from L^2 periodic functions. We define a quasiperiodic function as a superposition of periodic functions with incommensurate frequencies. As it turns out, sliding window embeddings of quasiperiodic functions are dense in high dimensional tori. In this talk, I will present some results for the quasiperiodic case.

17491

Wednesday 3/13 4:10 PM

Jonas Lührmann, Johns Hopkins

Local smoothing estimates for Schrödinger equations on hyperbolic space and applications
 Jonas Lührmann, Johns Hopkins
 Local smoothing estimates for Schrödinger equations on hyperbolic space and applications
 03/13/2019
 4:10 PM  5:00 PM
 C517 Wells Hall
We establish frequencylocalized local smoothing estimates for Schrödinger equations on hyperbolic space. The proof is based on the positive commutator method and a heat flow based LittlewoodPaley theory. Our results and techniques are motivated by applications to the problem of stability of solitary waves to nonlinear Schrödingertype equations on hyperbolic space.
The talk is based on joint work with Andrew Lawrie, SungJin Oh, and Sohrab Shahshahani.

17550

Thursday 3/14 3:00 PM

Linhui Shen, MSU

Cluster structure on moduli spaces of local systems for general groups
 Linhui Shen, MSU
 Cluster structure on moduli spaces of local systems for general groups
 03/14/2019
 3:00 PM  4:00 PM
 C204A Wells Hall
There have been several references in the literature devoted to the study of the cluster structures on moduli spaces of Glocal systems, all of which are based on case by case study. In this talk, we present a systematic construction that works for all groups at once. As an application, we will investigate the principal series representations of quantum groups from the perspective of cluster theory.

17542

Thursday 3/14 5:30 PM

AMS Student Chapter, MSU

Math trivia night
 AMS Student Chapter, MSU
 Math trivia night
 03/14/2019
 5:30 PM  7:30 PM
 C204 Wells Hall
The AMS Student Chapter is hosting a math trivia night on pi day! Please join us for a potluck and a lot of fun.

17534

Friday 3/15 4:10 PM

Peter Magyar, MSU

Necklaces, finite fields, and Lie algebras
 Peter Magyar, MSU
 Necklaces, finite fields, and Lie algebras
 03/15/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
The classical necklace problem asks, given q possible colors of beads, how many ways to string n beads around a necklace, counting rotations as the same. This has a nice solution using Mobius inversion from number theory. Amazingly, necklaces also give a way to picture the elements of a finite field with q^n elements, as well as a basis of the free Lie algebra with q generators.

17557

Monday 3/18 1:40 PM

Wenzhao Chen, MSU

Casson's invariant for oriented integer homology spheres
 Wenzhao Chen, MSU
 Casson's invariant for oriented integer homology spheres
 03/18/2019
 1:40 PM  3:00 PM
 C304 Wells Hall
This talk is an exposition of Casson's invariant: we will cover the definition of Casson's invariant in terms of Heegaard decomposition and representation spaces, and show how it can be computed (and defined) in terms of the Alexander polynomial of knots.

17558

Monday 3/18 3:00 PM

SuoJun Tan, MSU

Local Class Field Theory is Easy! Part I: Introduction
 SuoJun Tan, MSU
 Local Class Field Theory is Easy! Part I: Introduction
 03/18/2019
 3:00 PM  4:00 PM
 C517 Wells Hall
Local class field theory is about classifying all abelian extensions over a base local
field (for instances Q_p , R, C). It turns out that this extrinsic data is completely determined by
the intrinsic properties of the base field. We will start by reviewing some basic number theory
facts. We will then discuss statements in local class field theory and see some interesting
examples. We assume a basic knowledge of commutative algebra, infinite Galois theory and
number theory.

17549

Tuesday 3/19 11:00 AM

Brent Nelson, Vanderbilt and MSU

Free Stein Information
 Brent Nelson, Vanderbilt and MSU
 Free Stein Information
 03/19/2019
 11:00 AM  12:00 PM
 C304 Wells Hall
Given a von Neumann algebra M equipped with a trace, any selfadjoint operator in M can be thought of as a noncommutative random variable. For an ntuple X of such operators, the free Stein information of X is a free probabilistic quantity defined by the behavior of a noncommutative Jacobian on the polynomial algebra generated by entries of X. It is a number in the interval [0,n] and its value can provide information about the entries of X as well as the von Neumann algebra they generate. In this talk, I will discuss these and other properties of the free Stein information and consider a few examples where it can be explicitly computed. This is based on joint work with Ian Charlesworth.

17552

Wednesday 3/20 12:00 PM

Monica Karunakaran, MSU

A Strategy for Addressing Elementary Pre–Service Teachers’ Mathematics Anxiety
 Monica Karunakaran, MSU
 A Strategy for Addressing Elementary Pre–Service Teachers’ Mathematics Anxiety
 03/20/2019
 12:00 PM  1:00 PM
 133F Erick
Mathematics anxiety among elementary preservice teachers is a well–documented phenomenon that greatly affects their ability to engage in teacher preparation courses (e.g., Dutton, 1951; Gresham, 2007; Sloan, 2010). One way for instructors to engage with PSTs is to interact with them informally (Lamport, 1993). Informal conversations present an opportunity to increase students’ confidence and address their anxiety regarding mathematics content. A potential venue for informal conversations is office hours; however, college students often do not take advantage of office hours that are offered. This talk will describe preliminary results of a policy designed to increase instances of informal interactions between students and their instructors during office hours, by solely providing homework solutions to students during office hours. Initial evidence from surveys and course evaluations suggests that students who come into office hours engage with the instructor on topics they did not intend to discuss before coming to office hours, and suggests that these conversations have the potential to help reduce mathematics anxiety.

17559

Thursday 3/21 3:00 PM

Shlomo Levental, MSU

Poincare type inequalities via 1dimensional Malliavin calculus
 Shlomo Levental, MSU
 Poincare type inequalities via 1dimensional Malliavin calculus
 03/21/2019
 3:00 PM  3:50 PM
 C405 Wells Hall
We will review briefly 3 types of operators which are mapping spaces of realvalued functions which are defined on the real line equipped with standard normal probability measure. Those are the derivative, divergence and OrnsteinUklenbeck operators. There are simple formulas that describe the relationships between those operators. Using those formulas the proofs of the following will be presented:
1. Poincare inequality : The variance of a function of N(0,1) is dominated by the second moment of its derivative.
2. An upper bound to the Wasserstein distance between the distribution of a function of N(0,1) (the function has mean 0 and standard deviation 1) and N(0,1) itself. This upper bound is (up to a constant) the multiplication of the L4 norm of the function derivative and the L4 norm of the function 2nd derivative.
The material is based on Nourdin and Peccati book.

17560

Thursday 3/21 3:00 PM

Daping Weng, MSU

Cluster Structures on Double BottSamelson Cells
 Daping Weng, MSU
 Cluster Structures on Double BottSamelson Cells
 03/21/2019
 3:00 PM  4:00 PM
 C204A Wells Hall
Let $G$ be a KacPeterson group associated to a symmetrizable generalized Cartan matrix. Let $(b, d)$ be a pair of positive
braids associated to the root system. We define the double BottSamelson cell associated to $G$ and $(b,d)$ to be the moduli space of configurations of flags satisfying certain relative position conditions. We prove that they are affine varieties and their coordinate rings are upper cluster algebras. We construct the DonaldsonThomas transformation on double BottSamelson cells and show that it is a cluster transformation. In the cases where $G$ is semisimple and the positive braid $(b,d)$ satisfies a certain condition, we prove a periodicity result of the DonaldsonThomas transformation, and as an application of our periodicity result, we obtain a new geometric proof of Zamolodchikov's periodicity conjecture in the cases of $D\otimes A_n$. This is joint work with Linhui Shen.

14368

Thursday 3/21 4:10 PM

Wilfrid Gangbo, University of California, Los Angeles

A weaker notion of convexity for Lagrangians not depending solely on velocities and positions
 Wilfrid Gangbo, University of California, Los Angeles
 A weaker notion of convexity for Lagrangians not depending solely on velocities and positions
 03/21/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
In dynamical systems, one often encounters actions $\mathcal{A}\equiv \int_{\Omega}L(x, v(x))\rho dx$ which depend only on $v$, the velocity of the system and on $\rho$ the distribution of the particles. In this case, it is well–understood that convexity of $L(x, \cdot)$ is the right notion to study variational problems. In this talk, we consider a weaker notion of convexity which seems appropriate when the action depends on other quantities such as electro–magnetic fields. Thanks to the introduction of a gauge, we will argue why our problem reduces to understanding the relaxation of a functional defined on the set of differential forms (Joint work with B. Dacorogna).

18563

Monday 3/25 1:40 PM

Gorapada Bera, MSU

Taubes' approach to Casson Invariant
 Gorapada Bera, MSU
 Taubes' approach to Casson Invariant
 03/25/2019
 1:40 PM  2:50 PM
 C517 Wells Hall
No abstract available.

17541

Monday 3/25 4:10 PM

Paul Irving and Daryl McPadden , Physics, MSU

Group based assessments
 Paul Irving and Daryl McPadden , Physics, MSU
 Group based assessments
 03/25/2019
 4:10 PM  5:00 PM
 C109 Wells Hall
No abstract available.

17546

Tuesday 3/26 3:00 PM

Huyi Hu, MSU

The essential coexistence phenomenon in Hamiltonian dynamics
 Huyi Hu, MSU
 The essential coexistence phenomenon in Hamiltonian dynamics
 03/26/2019
 3:00 PM  4:00 PM
 C117 Wells Hall
We construct an example of a Hamiltonian flow $f^t$ on a $4$dimensional smooth manifold $\mathcal{M}$ which after being restricted to an energy surface $\mathcal{M}_e$ demonstrates essential coexistence of regular and chaotic dynamics, that is, there is an open and dense $f^t$invariant subset $U\subset\mathcal{M}_e$ such that the restriction $f^tU$ has nonzero Lyapunov exponents in all directions (except the direction of the flow) and is a Bernoulli flow while on the boundary $\partial U$, which has positive volume, all Lyapunov exponents of the system are zero.
This is a continuation of the talk given in previous weeks.

17492

Wednesday 3/27 4:10 PM

Yash Jhaveri, Institute for Advanced Study

Higher Regularity of the Singular Set in the Thin Obstacle Problem
 Yash Jhaveri, Institute for Advanced Study
 Higher Regularity of the Singular Set in the Thin Obstacle Problem
 03/27/2019
 4:10 PM  5:00 PM
 C517 Wells Hall
In this talk, I will give an overview of some of what is known about solutions to the thin obstacle problem, and then move on to a discussion of a higher regularity result on the singular part of the free boundary. This is joint work with Xavier FernándezReal.

17522

Wednesday 3/27 4:10 PM

Dongsoo Lee

Knot Floer homology obstructs ribbon concordance
 Dongsoo Lee
 Knot Floer homology obstructs ribbon concordance
 03/27/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
Zemke shows that the map on knot Floer homology induced by a ribbon concordance is injective in his paper.
I will be talking about its applications and proof.

18564

Thursday 3/28 3:00 PM

Daping Weng, MSU

Cluster Structures on Double BottSamelson Cells
 Daping Weng, MSU
 Cluster Structures on Double BottSamelson Cells
 03/28/2019
 3:00 PM  4:00 PM
 C204A Wells Hall
Let $G$ be a KacPeterson group associated to a symmetrizable generalized Cartan matrix. Let $(b, d)$ be a pair of positive
braids associated to the root system. We define the double BottSamelson cell associated to $G$ and $(b,d)$ to be the moduli space of configurations of flags satisfying certain relative position conditions. We prove that they are affine varieties and their coordinate rings are upper cluster algebras. We construct the DonaldsonThomas transformation on double BottSamelson cells and show that it is a cluster transformation. In the cases where $G$ is semisimple and the positive braid $(b,d)$ satisfies a certain condition, we prove a periodicity result of the DonaldsonThomas transformation, and as an application of our periodicity result, we obtain a new geometric proof of Zamolodchikov's periodicity conjecture in the cases of $D\otimes A_n$. This is joint work with Linhui Shen.

18567

Thursday 3/28 3:00 PM

Roger Lee, University of Chicago

Variance Swaps on TimeChanged Markov Processes
 Roger Lee, University of Chicago
 Variance Swaps on TimeChanged Markov Processes
 03/28/2019
 3:00 PM  3:50 PM
 C405 Wells Hall
We prove that a variance swap has the same price as a coterminal Europeanstyle contract, when the underlying is a Markov process, timechanged by a general continuous stochastic clock, which is allowed to have general correlation with the driving Markov process, which is allowed to have statedependent jump distributions. The European contract’s payoff function satisfies an ordinary integrodifferential equation, which depends only on the dynamics of the Markov process, not on the clock. In some examples, the payoff function that prices the variance swap can be computed explicitly. Joint work with Peter Carr and Matt Lorig.

14365

Thursday 3/28 4:10 PM

Ken Ono, Emory University

Jensen–Polya Program for the Riemann Hypothesis and Related Problems
 Ken Ono, Emory University
 Jensen–Polya Program for the Riemann Hypothesis and Related Problems
 03/28/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
In 1927 Polya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann’s Xifunction. This hyperbolicity had only been proved for degrees $d=1,2,3$. We prove the hyperbolicity of all (but possibly finitely many) the Jensen polynomials of every degree $d$. Moreover, we establish the outright hyperbolicity for all degrees $d< 10^{26}$. These results follow from an unconditional proof of the "derivative aspect" GUE distribution for zeros. This is joint work with Michael Griffin, Larry Rolen, and Don Zagier.

18569

Friday 3/29 2:00 PM

Zheng Xiao, MSU

MordellWeil Theorem: Part III
 Zheng Xiao, MSU
 MordellWeil Theorem: Part III
 03/29/2019
 2:00 PM  4:00 PM
 C204A Wells Hall
No abstract available.

17556

Friday 3/29 4:10 PM

Ken Ono, Emory University

Distinguished Undergraduate Lecture: Why Does Ramanujan, “The Man Who Knew Infinity,” Matter?
 Ken Ono, Emory University
 Distinguished Undergraduate Lecture: Why Does Ramanujan, “The Man Who Knew Infinity,” Matter?
 03/29/2019
 4:10 PM  5:00 PM
 B119 Wells Hall
Srinivasa Ramanujan, one of the most inspirational figures in the history of mathematics, was a poor gifted mathematician from lush south India who left behind three notebooks that engineers, mathematicians, and physicists continue to mine today. Born in 1887, Ramanujan was a twotime college dropout. He could have easily been lost to the world, a thought that scientists cannot begin to absorb. He died in 1920. Prof. Ono will explain why Ramanujan matters today, and will share several clips from the film, “The Man Who Knew Infinity,” starring Dev Patel and Jeremy Irons. Professor Ono served as an associate producer and mathematical consultant for the film.
Bio: Ken Ono is the Asa Griggs Candler Professor of Mathematics at Emory University and the Vice President of the American Mathematical Society. He is considered to be an expert in the theory of integer partitions and modular forms. He has been invited to speak to audiences all over North America, Asia and Europe. His contributions include several monographs and over 170 research and popular articles in number theory, combinatorics and algebra. He received his Ph.D. from UCLA and has received many awards for his research in number theory, including a Guggenheim Fellowship, a Packard Fellowship and a Sloan Fellowship. He was awarded a Presidential Early Career Award for Science and Engineering (PECASE) by Bill Clinton in 2000 and he was named the National Science Foundation’s Distinguished Teaching Scholar in 2005. In addition to being a thesis advisor and postdoctoral mentor, he has also mentored dozens of undergraduates and high school students. He serves as EditorinChief for several journals and is an editor of The Ramanujan Journal. He was also an associate producer of the 2016 Hollywood film “The Man Who Knew Infinity” which starred Jeremy Irons and Dev Patel.

18568

Monday 4/1 1:40 PM

Keshav Sutrave, MSU

Stability theorems for YangMills fields
 Keshav Sutrave, MSU
 Stability theorems for YangMills fields
 04/01/2019
 1:40 PM  3:00 PM
 C517 Wells Hall
BourguignonLawson's 1981 paper.

18572

Monday 4/1 3:00 PM

Nick Rekuski, MSU

Minimal Free Resolutions
 Nick Rekuski, MSU
 Minimal Free Resolutions
 04/01/2019
 3:00 PM  4:00 PM
 C517 Wells Hall
The Hilbert function is a classical invariant of a variety (with a given embedding) that is easy to compute. It determines some properties of the variety (such as degree, dimension, and arithmetic genus), but it cannot determine more sophisticated invariants. A minimal free resolution determines more sophisticated properties of the variety while still being easily computable. For example, any set of seven points in P^3 in linearly general position has the same Hilbert function, but minimal free resolutions can distinguish whether the points lie on a rational normal curve. Furthermore, a minimal free resolution retains all the information of the Hilbert function. In this talk, we will define a minimal free resolution and associated invariants. With the definitions in place, we will show that minimal free resolutions retain all the information of the Hilbert function then explain the above example. If time permits, we will additionally show that minimal free resolutions are well behaved when restricting a variety to a hypersurface.

17538

Thursday 4/4 2:00 PM

Leonid Chekhov, MSU

$SL_k$ character varieties and quantum cluster algebras
 Leonid Chekhov, MSU
 $SL_k$ character varieties and quantum cluster algebras
 04/04/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
briefly recall a combinatorial approach to the description and quantization of Teichmuller spaces of Riemann surfaces $\Sigma_{g,s}$ of genus $g$ with $s$ holes and algebras of geodesic functions on these surfaces. We describe sets of geodesic functions in W.Thurston shear coordinates based on an ideal triangle decomposition of Riemann surfaces with holes and demonstrate the polynomiality and positivity properties of the corresponding geodesic functions. In the algebraic setting, these sets are related to traces of monodromies of $SL_2$ connection on $\Sigma_{g,s}$, and Darbouxtype Poisson and quantum relations on shear coordinates were proven to generate Goldman brackets on geodesic functions. I will describe these structures and their recent generalizations to $SL_2$ and $SL_n$ (decorated) character varieties on Riemann surfaces $\Sigma_{g,s,n}$ with holes and $n$ marked points on hole boundaries and how it is interlaced with cluster algebras, reflection equations, and groupoids of upper triangular matrices. [Based on work in collaboration with M.Mazzocco, V.Roubtsov, and M.Shapiro.]

17551

Thursday 4/4 3:00 PM

John Machacek, York University

Sign variation and boundary measurement in projective space
 John Machacek, York University
 Sign variation and boundary measurement in projective space
 04/04/2019
 3:00 PM  4:00 PM
 C204A Wells Hall
We are interested in the topology of some spaces obtained by relaxing total positivity in the real Grassmannian. We define two families of subsets of the Grassmannian each of which include both the totally nonnegative Grassmannian and the whole Grassmannian. In this initial study of such subsets of the Grassmannian we focus of subsets of real projective space where interesting topology already appears. We we are able to find a regular CW complex which can be leveraged to compute some invariants like the fundamental group and Euler characteristic. We also conjecture some "balllike" properties (e.g. CohenMacualayness).

18573

Thursday 4/4 3:00 PM

Alexander Schnurr, University Siegen (Germany)

Ordinal Patterns in Clusters of Extremes of Regularly Varying Time Series
 Alexander Schnurr, University Siegen (Germany)
 Ordinal Patterns in Clusters of Extremes of Regularly Varying Time Series
 04/04/2019
 3:00 PM  3:50 PM
 C405 Wells Hall
The purpose is to investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and the ordinal patterns within a cluster. The latter have been introduced in order to handle data sets with several thousand data points appearing in medicine, biology, finance and computer science. Since these patterns take only the ordinal structure of consecutive data points into account, the method is robust under monotone transformations and measurement errors. We verify the existence of the corresponding limit distributions in the framework of regularly varying time series, develop nonparametric estimators and show and their asymptotic normality under appropriate mixing conditions. (This is joint work with Marco Oesting.)

18570

Friday 4/5 4:10 PM

Guang Lin, Purdue University

Uncertainty Quantification and Machine Learning of the Physical Laws Hidden Behind the Noisy Data
 Guang Lin, Purdue University
 Uncertainty Quantification and Machine Learning of the Physical Laws Hidden Behind the Noisy Data
 04/05/2019
 4:10 PM  5:00 PM
 1502 Engineering Building
In this talk, I will present a new datadriven paradigm on how to quantify the structural uncertainty (modelform uncertainty) and learn the physical laws hidden behind the noisy data in the complex systems governed by partial differential equations. The key idea is to identify the terms in the underlying equations and to approximate the coefficients of the terms with error bars using Bayesian machine learning algorithms on the available noisy measurement. In particular, Bayesian sparse feature selection and parameter estimation are performed. Numerical experiments show the robustness of the learning algorithms with respect to noisy data and size, and its ability to learn various candidate equations with error bars to represent the quantified uncertainty.

18574

Monday 4/8 1:40 PM

Keshav Sutrave, MSU

Stability theorems for YangMills fields (continued)
 Keshav Sutrave, MSU
 Stability theorems for YangMills fields (continued)
 04/08/2019
 1:40 PM  3:00 PM
 C517 Wells Hall
Talk II on BourguignonLawson's 1978 paper

17510

Monday 4/8 3:00 PM

Mona Merling, University of Pennsylvania

The equivariant stable parametrized hcobordism theorem
 Mona Merling, University of Pennsylvania
 The equivariant stable parametrized hcobordism theorem
 04/08/2019
 3:00 PM  4:00 PM
 C304 Wells Hall
The stable parametrized hcobordism theorem provides a critical link in the chain of homotopy theoretic constructions that show up in the classification of manifolds and their diffeomorphisms. For a compact smooth manifold M it gives a decomposition of Waldhausen's A(M) into QM_+ and a delooping of the stable hcobordism space of M. I will talk about joint work with Malkiewich on this story when M is a smooth compact Gmanifold.

18571

Wednesday 4/10 3:00 PM

Zhenqi Wang, MSU

New examples of local rigidity of solvable algebraic partially hyperbolic actions
 Zhenqi Wang, MSU
 New examples of local rigidity of solvable algebraic partially hyperbolic actions
 04/10/2019
 3:00 PM  4:00 PM
 C117 Wells Hall
We show $C^\infty$ local rigidity for a broad class of new examples of solvable algebraic partially hyperbolic actions on ${\mathbb G}=\mathbb{G}_1\times\cdots\times \mathbb{G}_k/\Gamma$, where $\mathbb{G}_1$ is of the following type: $SL(n, {\mathbb R})$, $SO_o(m,m)$, $E_{6(6)}$, $E_{7(7)}$ and $E_{8(8)}$, $n\geq3$, $m\geq 4$. These examples include rankone partially hyperbolic actions. The method of proof is a combination of KAM type iteration scheme and representation theory. The principal difference with previous work
that used KAM scheme is very general nature of the proof: no specific information about unitary representations of ${\mathbb G}$ or ${\mathbb G}_1$ is required.
This is a continuation of the last talk.

17524

Wednesday 4/10 4:10 PM

Joe Melby

Knot Genus and Complexity
 Joe Melby
 Knot Genus and Complexity
 04/10/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
A classical problem in knot theory is determining whether or not a given 2dimensional diagram represents the unknot. The UNKNOTTING PROBLEM was proven to be in NP by Hass, Lagarias, and Pippenger. A generalization of this decision problem is the GENUS PROBLEM. We will discuss the basics of computational complexity, knot genus, and normal surface theory in order to present an algorithm (from HLP) to explicitly compute the genus of a knot. We will then show that this algorithm is in PSPACE and discuss more recent results and implications in the field.

17498

Thursday 4/11 2:00 PM

Jennifer Hom, Georgia Tech

Heegaard Floer and homology cobordism
 Jennifer Hom, Georgia Tech
 Heegaard Floer and homology cobordism
 04/11/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
We show that the threedimensional homology cobordism group admits an infiniterank summand. It was previously known that the homology cobordism group contains an infiniterank subgroup and a Zsummand. The proof relies on the involutive Heegaard Floer homology package of HendricksManolescu and HendricksManolescuZemke. This is joint work with I. Dai, M. Stoffregen, and L. Truong.

18576

Friday 4/12 2:00 PM

Nick Rekuski, MSU

FarguesFontaine Curve: Part I
 Nick Rekuski, MSU
 FarguesFontaine Curve: Part I
 04/12/2019
 2:00 PM  4:00 PM
 C204A Wells Hall
There is a close analogy between function fields over finite fields and number fields. In this analogy $\text{Spec } \mathbb{Z}$ corresponds to an algebraic curve over a finite field. However, this analogy often fails. For example, $\text{Spec } \mathbb{Z} \times \text{Spec } \mathbb{Z} $ (which should correspond to a surface) is $\text{Spec } \mathbb{Z}$ (which corresponds to a curve). In many cases, the FarguesFontaine curve is the natural analogue for algebraic curves. In this first talk, we will give the construction of the FarguesFontaine curve.

18575

Friday 4/12 4:10 PM

Fernando Guevara Vasquez, University of Utah

Manipulation of particles in a fluid with standing acoustic waves
 Fernando Guevara Vasquez, University of Utah
 Manipulation of particles in a fluid with standing acoustic waves
 04/12/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
Consider a collection of particles in a fluid that is subject to
a standing acoustic wave. In some situations, the particles tend to
cluster about the nodes of the wave. We study the problem of finding a
standing acoustic wave that can position particles in desired locations,
i.e. whose nodal set is as close as possible to desired curves or
surfaces. We show that in certain situations we can expect to reproduce
patterns up to the diffraction limit. For periodic particle patterns, we
show that there are limitations on the unit cell and that the possible
patterns in dimension d can be determined from an eigendecomposition of a
2d x 2d matrix.

18578

Monday 4/15 1:45 PM

Tom Parker, MSU

A short proof of the Gromov Convergence theorem for Jholomorphic maps
 Tom Parker, MSU
 A short proof of the Gromov Convergence theorem for Jholomorphic maps
 04/15/2019
 1:45 PM  3:00 PM
 C517 Wells Hall
No abstract available.

18562

Monday 4/15 4:10 PM

Round Table Discussion

Faculty Teaching Observations & Evaluation
 Round Table Discussion
 Faculty Teaching Observations & Evaluation
 04/15/2019
 4:10 PM  5:00 PM
 C109 Wells Hall
No abstract available.

17525

Wednesday 4/17 4:10 PM

Gorapada Bera

Introduction to Seiberg Witten invariants on three manifolds
 Gorapada Bera
 Introduction to Seiberg Witten invariants on three manifolds
 04/17/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
Although Seiberg Witten invariant originally introduced for four manifolds, but its three dimensional version is also interesting .After a brief discussion on the definition of the Seiberg Witten invariant on three manifolds we will see some results from literature equating this invariant to some known invariants of three manifolds.

18566

Thursday 4/18 2:00 PM

Robert Bell, MSU

Quasipositivity in free groups and braid groups
 Robert Bell, MSU
 Quasipositivity in free groups and braid groups
 04/18/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
I'll discuss joint work with Rita Gitik (UM) on the problem of recognizing quasipositive elements of a group G defined by
a finite presentation (X ; R). An element of G is quasipositive if it can be represented by a word that is a product of conjugates of positive powers of letters in X. The recognition problem is to determine whether or not a given word (using both positive and negative powers of letters in X) represents an element of G that is quasipositive. This problem was solved by Orevkov when G is free with basis X or when G is the 3strand braid group with its standard generating set. I'll present a new solution to the recognition problem for free groups and discuss some of the challenges posed by braid groups and related groups.

18579

Thursday 4/18 3:00 PM

Michael Shapiro, MSU

Cluster algebras with Grassmann variables (joint with V. Ovsienko)
 Michael Shapiro, MSU
 Cluster algebras with Grassmann variables (joint with V. Ovsienko)
 04/18/2019
 3:00 PM  4:00 PM
 C117 Wells Hall
We develop a version of cluster algebra extending the ring of Laurent polynomials by adding Grassmann variables. These algebras can be described in terms of “extended quivers” which are oriented hypergraphs. We describe mutations of such objects and deﬁne a corresponding commutative superalgebra. Our construction includes the notion of weighted quivers that has already appeared in diﬀerent contexts. This project is a step towards understanding the notion of cluster superalgebra.

15385

Thursday 4/18 4:10 PM

Emmy Murphy, Northwestern University

Flexibility in contact and symplectic geometry
 Emmy Murphy, Northwestern University
 Flexibility in contact and symplectic geometry
 04/18/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
We discuss a number of $h$principle phenomena which were recently discovered in the field of contact and symplectic geometry. In generality, an $h$principle is a method for constructing global solutions to underdetermined PDEs on manifolds by systematically localizing boundary conditions. In symplectic and contact geometry, these strategies typically are well suited for general constructions and partial classifications. Some of the results we discuss are the characterization of smooth manifolds admitting contact structures, high dimensional overtwistedness, the symplectic classification of flexible Stein manifolds, and the construction of exotic Lagrangians in $C^n$.

18577

Friday 4/19 2:00 PM

Nick Rekuski, MSU

FarguesFontaine Curve: Part II
 Nick Rekuski, MSU
 FarguesFontaine Curve: Part II
 04/19/2019
 2:00 PM  4:00 PM
 C204A Wells Hall
No abstract available.

18565

Monday 4/22 1:45 PM

Jon Wolfson, MSU

TBA
 Jon Wolfson, MSU
 TBA
 04/22/2019
 1:45 PM  3:00 PM
 C517 Wells Hall
No abstract available.

15449

Monday 4/22 4:10 PM

Jane Zimmerman, MSU

MTH 103A/B: Experiences from the classroom and future directions
 Jane Zimmerman, MSU
 MTH 103A/B: Experiences from the classroom and future directions
 04/22/2019
 4:10 PM  5:00 PM
 C109 Wells Hall
No abstract available.

17493

Wednesday 4/24 4:10 PM

Nestor Guillen, University of Massachusetts at Amherst

Transportation methods for Lévy measures and applications
 Nestor Guillen, University of Massachusetts at Amherst
 Transportation methods for Lévy measures and applications
 04/24/2019
 4:10 PM  5:00 PM
 C517 Wells Hall
The comparison principle for second order elliptic equations is one of the cornerstone of the theory of viscosity solutions. Works of Sayah and more recently by JakobsenKarlsen and BarlesImbert have expanded it to many important subfamilies of nonlocal elliptic equations. In joint work with Chenchen Mou and Andrzej Święch we show how optimal transportation methods can be used to couple Lévy measures, which encode the integrodifferential part of nonlocal operators, which allow us to obtain comparison principles for new families of nonlocal equations. Our method puts all previous subfamilies of nonlocal operators (LevyIto operators, operators of order less than 1) in a single framework, while also yielding results for new families.

14350

Thursday 4/25 4:10 PM

André Neves, University of Chicago

TBA
 André Neves, University of Chicago
 TBA
 04/25/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
No abstract available.
