| Talk_id | Date | Speaker | Title |
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17497
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Monday 1/7
4:10 PM
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Matthew Ballard, University of South Carolina
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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.
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17495
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Wednesday 1/9
4:10 PM
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Eugenia Malinnikova, Norwegian University of Science and Technology
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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 Laplace-Beltrami operator on compact manifolds.
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17501
|
Friday 1/11
4:10 PM
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Pavlo Pylyavskyy, University of Minnesota
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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
T-systems 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, Wronskian-Casoratian duality in ODE, gauge/string theories, etc. Periodicity of certain T-systems 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 T-systems, 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 T-systems 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 Kazhdan-Lusztig theory for dihedral groups, the other two classifications are new. This is joint work with Pavel Galashin.
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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 volume-preserving 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 Navier-Stokes and 3D hyperviscous Navier-Stokes on the periodic box. The work in this talk is joint with Jacob Bedrossian, Samuel Punshon-Smith, Jinxin Xue and Lai-Sang Young.
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17502
|
Wednesday 1/16
1:40 PM
|
Goncalo Oliveira, Universidade Federal Fluminense, Rio de Janeiro
|
Gauge theory on Aloff-Wallach spaces
- Goncalo Oliveira, Universidade Federal Fluminense, Rio de Janeiro
- Gauge theory on Aloff-Wallach spaces
- 01/16/2019
- 1:40 PM - 3:00 PM
- C517 Wells Hall
I will describe joint work with Gavin Ball constructing and classifying G2-instantons on Aloff-Wallach spaces, which are the most interesting known examples of compact "nearly-parallel" G2-manifolds.
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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.
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17506
|
Thursday 1/17
3:00 PM
|
Daping , MSU
|
More on Scattering Diagram and Theta Functions
- Daping , 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 Gross-Hacking-Keel-Kontsevich’s proofs of positive Laurent phenomenon, sign coherence, and a weak version of the cluster duality conjecture.
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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.
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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 tight-binding 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 self-similar 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 self-similarity 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.
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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.
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16468
|
Thursday 1/24
2:00 PM
|
Rebecca Winarski, University of Michigan
|
TBA
- Rebecca Winarski, University of Michigan
- TBA
- 01/24/2019
- 2:00 PM - 3:00 PM
- C304 Wells Hall
TBA
|
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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.
|
|
15449
|
Monday 1/28
4:10 PM
|
Jane Zimmerman, MSU
|
MTH 103A: Experiences from the classroom and future directions
- Jane Zimmerman, MSU
- MTH 103A: Experiences from the classroom and future directions
- 01/28/2019
- 4:10 PM - 5:00 PM
- C109 Wells Hall
No abstract available.
|
|
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.
|
|
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.
|
|
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 Deligne-Mumford 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 Matsuzaki-Yabuki-Jaerisch 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.
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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.
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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.
|
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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.
|
|
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.
|
