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.

16478

Wednesday 2/6 4:10 PM

Mihai Tohaneanu, University of Kentucky

TBA
 Mihai Tohaneanu, University of Kentucky
 TBA
 02/06/2019
 4:10 PM  5:00 PM
 C517 Wells Hall
No abstract available.

15394

Thursday 2/7 2:00 PM

Adam Sikora, SUNY at Buffalo

TBA
 Adam Sikora, SUNY at Buffalo
 TBA
 02/07/2019
 2:00 PM  3:00 PM
 C304 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

TBA
 Albert Ai, UC Berkeley
 TBA
 02/13/2019
 4:10 PM  5:00 PM
 C517 Wells Hall
TBA

17499

Thursday 2/14 2:00 PM

Melissa Zhang, Boston College

TBA
 Melissa Zhang, Boston College
 TBA
 02/14/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
No abstract available.

17507

Thursday 2/14 3:00 PM

Salvatore Stella, University of Haifa

TBA
 Salvatore Stella, University of Haifa
 TBA
 02/14/2019
 3:00 PM  4:00 PM
 C117 Wells Hall
No abstract available.

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.

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.

17509

Thursday 2/28 2:00 PM

Eva Belmont, Northwestern University

TBA
 Eva Belmont, Northwestern University
 TBA
 02/28/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
No abstract available.

17491

Wednesday 3/13 4:10 PM

Jonas Lührmann, Johns Hopkins

TBA
 Jonas Lührmann, Johns Hopkins
 TBA
 03/13/2019
 4:10 PM  5:00 PM
 C517 Wells Hall
No abstract available.

15423

Thursday 3/14 2:00 PM

Luca Spolaor, Massachusetts Institute of Technology

TBA
 Luca Spolaor, Massachusetts Institute of Technology
 TBA
 03/14/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
No abstract available.

14369

Thursday 3/14 4:10 PM

Jacob Tsimerman, University of Toronto

TBA
 Jacob Tsimerman, University of Toronto
 TBA
 03/14/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
No abstract available.

14368

Thursday 3/21 4:10 PM

Wilfrid Gangbo, University of California, Los Angeles

TBA
 Wilfrid Gangbo, University of California, Los Angeles
 TBA
 03/21/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
No abstract available.

17492

Wednesday 3/27 4:10 PM

Yash Jhaveri, Institute for Advanced Study

TBA
 Yash Jhaveri, Institute for Advanced Study
 TBA
 03/27/2019
 4:10 PM  5:00 PM
 C517 Wells Hall
No abstract available.

14365

Thursday 3/28 4:10 PM

Ken Ono, Emory University

TBA
 Ken Ono, Emory University
 TBA
 03/28/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
No abstract available.

17510

Monday 4/8 3:00 PM

Mona Merling, University of Pennsylvania

TBA
 Mona Merling, University of Pennsylvania
 TBA
 04/08/2019
 3:00 PM  4:00 PM
 C304 Wells Hall
No abstract available.

17498

Thursday 4/11 2:00 PM

Jennifer Hom, Georgia Tech

TBA
 Jennifer Hom, Georgia Tech
 TBA
 04/11/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
No abstract available.

14377

Thursday 4/11 4:10 PM

Francesco Maggi, The University of Texas at Austin

TBA
 Francesco Maggi, The University of Texas at Austin
 TBA
 04/11/2019
 4:10 PM  5:00 PM
 C304 Wells Hall
No abstract available.

15385

Thursday 4/18 4:10 PM

Emmy Murphy, Northwestern University

TBA
 Emmy Murphy, Northwestern University
 TBA
 04/18/2019
 4:10 PM  5:00 PM
 C304 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.

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.
