| Date: | February 2, 2024 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | Youngho Yoo, TAMU |
| Title: | Minimum degree conditions for apex-outerplanar minors |
| Abstract: | Motivated by Hadwiger's conjecture, we study graphs H for which every graph with minimum degree at least |V(H)|-1 contains H as a minor. We prove that a large class of apex-outerplanar graphs satisfies this property. Our result gives the first examples of such graphs whose vertex cover numbers are significantly larger than a half of its vertices, and recovers all known such graphs that have arbitrarily large maximum degree. Our proof can be adapted to directed graphs to show that every directed graph with minimum out-degree at least t contains a certain orientation of the wheel and of every apex-tree on t+1 vertices as a subdivision and a butterfly minor respectively. Joint work with Chun-Hung Liu.
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| Date: | February 9, 2024 |
| Time: | 4:00pm |
| Location: | BLOC 302 |
| Speaker: | Tushar Pandey, TAMU |
| Title: | Invariants for surface diffeomorphisms and the volume conjecture |
| Abstract: | In this talk, we will discuss an invariant for the diffeomorphisms of a surface using the Chekhov-Fock algebra for surfaces. This invariant is a trace of an intertwiner coming from some representation theory of this algebra. We will then mention a conjecture that relates the exponential growth of the trace to the volume of the mapping torus of a surface. And at the end, we will see some recent results in this area. |
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| Date: | March 1, 2024 |
| Time: | 2:00pm |
| Location: | BLOC 302 |
| Speaker: | Alex Lubotzky, Weizmann Institute of Science |
| Title: | Uniform stability of high-rank Arithmetic groups |
| Abstract: | (Joint with the workshop "Groups and dynamics".)
Lattices in high-rank semisimple groups enjoy several special properties like super-rigidity, quasi-isometric rigidity, first-order rigidity, and more. In this talk, we will add another one: uniform ( a.k.a. Ulam) stability. Namely, it will be shown that (most) such lattices D satisfy: every finite-dimensional unitary "almost-representation" of D ( almost w.r.t. to a sub-multiplicative norm on the complex matrices) is a small deformation of a true unitary representation. This extends a result of Kazhdan (1982) for amenable groups and Burger-Ozawa-Thom (2013) for SL(n,Z), n>2.
The main technical tool is a new cohomology theory ("asymptotic cohomology") that is related to bounded cohomology in a similar way to the connection of the last one with ordinary cohomology. The vanishing of H^2 w.r.t. to a suitable module implies the above stability.
The talk is based on a joint work with L. Glebsky, N. Monod, and B. Rangarajan. |
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| Date: | March 22, 2024 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | Yifan Zhang, UT Austin |
| Title: | Covering Number of Real Algebraic Varieties and Beyond: Improved Bounds and Applications |
| Abstract: | In this talk, I will prove a new upper bound on the covering number of real algebraic varieties, images of polynomial maps and semialgebraic sets. The bound remarkably improves the best known general bound by Yomdin and Comte (2004), and its proof is much more straightforward. As a consequence, our result gives new bounds on the volume of the tubular neighborhood of the image of a polynomial map and a semialgebraic set, where results for varieties by Lotz (2015) and Basu, Lerario (2022) are not directly applicable. I will first use this result to derive a near-optimal bound on the covering number of low rank CP tensors. Then I will discuss applications on sketching (general) polynomial optimization problems as well as controlling the generalization error for deep neural networks with rational or ReLU activations. |
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| Date: | March 23, 2024 |
| Time: | 00:00am |
| Location: | Blocker |
| Title: | CombinaTexas 2024 |
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| Date: | March 24, 2024 |
| Time: | 00:00am |
| Location: | Blocker |
| Title: | CombinaTexas 2024 |
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| Date: | April 5, 2024 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | Chun-Hung Liu, TAMU |
| Title: | Asymptotically optimal proper conflict-free coloring of bounded maximum degree graphs |
| Abstract: | Every graph of maximum degree d has a coloring with d+1 colors such that no two adjacent vertices receive the same color. Caro, Petrusevski, Skrekovski conjectured that if d >2, then one can always choose such a proper (d+1)-coloring such that for every non-isolated vertex, some color appears on its neighborhood exactly once. We prove that this conjecture holds asymptotically: every graph of maximum degree d has a proper coloring with (1+o(1))d colors such that for every non-isolated vertex, some color appears on its neighborhood exactly once. Joint work with Bruce Reed. |
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| Date: | April 19, 2024 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | Matthew Faust, TAMU |
| Title: | Irreducibility of the Bloch Variety |
| Abstract: | Given a ZZ^d-periodic graph G, a discrete periodic operator, a periodic potential together with a weighted graph laplacian, acts on functions on the vertices of G. Floquet theory allows us to study the spectrum through a finite matrix with Laurent polynomials entries. The zero set of the corresponding characteristic polynomial is called the Bloch variety. We will focus our attention on the irreducibility of this variety, which provides insight into quantum ergodicity. In particular we study how irreducibility of the Bloch variety is affected as one varies the period of the potential. |
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| Date: | April 26, 2024 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | Hannah Solomon, TAMU |
| Title: | Classifying and realizing modular data for super-modular tensor categories |
| Abstract: | Super-modular tensor categories have broad applications, including to spin topological quantum field theories and fermionic topological phases of matter. However, the current classification is only confirmed to be complete through rank 6. We aim to further the classification and understand more about realizing the modular data produced through various methods as data coming from super-modular tensor categories. |
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