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4:00pm to 5:00pm - NS2 1201 - Geometry and Topology Yanir Rubinstein - (Maryland and Stanford) RTG Distinguished Lecture Talk 1: Invitation to Geometry via Mahler's Conjectures: a mathematical opera in three acts Act I: Convexity, Duality, and Volume |
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1:00pm to 2:00pm - RH 340N - Dynamical Systems Karl Zieber - (UCI) Spectral Gaps of Non-Stationary Random Matrix Products In classical (i.e., IID) random matrix dynamics, a question that arises frequently is whether the Lyapunov spectrum is "simple." There are several criteria that imply the existence of a maximal number of distinct Lyapunov exponents for random matrix products and these have been used in various applications. Recently, there have been papers extending this classical theory to specific classes of non-stationary matrix products. In this talk, we will discuss two recent papers ([arXiv:2312.03181] and [arXiv.2507.04058]) which establish gaps between non-stationary analogs of Lyapunov exponents. Strategies and key ideas will be presented, with a brief discussion about applications to Anderson localization. |
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3:00pm - RH306 - Differential Geometry Kuan-Hui Lee - (UQAM) Pluriclosed 3-folds with vanishing Bismut Ricci form In this talk, we discuss compact complex 3-dimensional non-K\"ahler Bismut Ricci flat pluriclosed Hermitian manifolds (BHE) via their dimensional reduction to a special K\"ahler geometry in complex dimension 2. The reduced geometry satisfies a 6th order non-linear PDE which has infinite dimensional momentum map interpretation, similar to the much studied K\"ahler metrics of constant scalar curvature (cscK). We use this to associate to the reduced manifold or orbifold Mabuchi and Calabi functionals, as well as to obtain obstructions for the existence of solutions in terms of the automorphism group, paralleling results by Futaki and Calabi--Lichnerowicz--Matsushima in the cscK case. Through the obstruction theorem, we show that the quotients of $SU(2)\times SU(2)$ or $SU(2)\times \mathbb{R}^3$ as the only non-K\"ahler BHE $3$-folds with $2$-dimensional Bott--Chern $(1,1)$-cohomology group, for which the reduced space is a smooth K\"ahler surface. Lastly, we discuss explicit solutions of the PDE on orthotoric K\"ahler orbifold surfaces which yield infinitely many non-K\"ahler BHE structures on $S^3\times S^3$ and $S^1\times S^2 \times S^3$. |
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3:00pm to 3:50pm - RH 440R - Logic Set Theory Julian Eshkol - (UC Irvine) Ineffable Ideals This is a continuation of a series of lectures showing the consistency of the existence of weakly ineffable ideals on successor cardinals. |
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4:00pm to 5:00pm - RH306 - Differential Geometry Yanir Rubinstein - (Maryland and Stanford) RTG Distinguished Lecture Talk 2: Invitation to Geometry via Mahler's Conjectures: a mathematical opera in three acts Act I: Convexity, Duality, and Volume |
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3:00pm to 4:00pm - RH 306 - Number Theory Jasmine Camero - (Emory University) Classifying Possible Density Degree Sets for Hyperelliptic Curves Let $C$ be a smooth, projective, geometrically integral hyperelliptic curve of genus $g \geq 2$ over a number field $k$. To study the distribution of degree $d$ points on $C$, we introduce the notion of $\mathbb{P}^1$- and AV-parameterized points, which arise from natural geometric constructions. These provide a framework for classifying density degree sets, an important invariant of a curve that records the degrees $d$ for which the set of degree $d$ points on $C$ is Zariski dense. Zariski density has two geometric sources: If $C$ is a degree $d$ cover of $\mathbb{P}^1$ or an elliptic curve $E$ of positive rank, then pulling back rational points on $\mathbb{P}^1$ or $E$ give an infinite family of degree $d$ points on $C$. Building on this perspective, we give a classification of the possible density degree sets of hyperelliptic curves. |