|
11:00am to 12:00pm - 340P - Machine Learning Peter Chang - (Departments of Radiological Sciences and Computer Science, UCI) How to Approach Deep Learning for Medical Data |
|
1:00pm - RH 340N - Harmonic Analysis Li Gao - (Wuhan University) Complex Interpolation in Quantum Information Many problems of error analysis in quantum information processing can be formulated as deviation inequalities of random matrices. In this talk, I will talk about how complex interpolations of various Lp spaces can be an effective tool in establishing error estimates in information tasks such as quantum soft covering, privacy amplification, convex splitting and quantum decoupling. This talk is based on joint works with Hao-Chung Cheng, Yu-Chen Shen, Frédéric Dupuis and Mario Berta. |
|
2:00pm - RH 340P - Nicolas Cuervo Ovalle - (Universidad de los Andes (visiting UCI)) Schröder-Bernstein property on metric structures-II (probability algebras) We say that a complete theory T has the Schröder-Bernstein property, or simply, the SB-property, if any two models M and N of T that are elementary bi-embeddable are isomorphic. The purpose of this talk is to study the SB-property for metric theories. This time we will focus our study on probability algebras and expansions by a generic automorphism. This is a joint work with Alexander Berenstein and Camilo Argoty presented in [1].
Reference [1] Argoty, C., Berenstein, A. & Cuervo Ovalle, N. The SB-property on metric structures. Arch. Math. Logic (2025). https://doi.org/10.1007/s00153-024-00949-y |
|
1:00pm to 2:00pm - RH 440R - Dynamical Systems Jake Fillman - (Texas A&M) The spectra of Schrodinger operators over hyperbolic toral tranformations We will discuss Schrodinger operators generated by hyperbolic transformations of tori and show that they cannot have any essential spectral gaps.The key ingredient is a topological argument using Johnson's gap-labelling theorem. |
|
3:00pm to 4:00pm - Rowland Hall 510R - Combinatorics and Probability Kewen Wu - (UC Berkeley) Locally Sampleable Uniform Symmetric Distributions We characterize the power of constant-depth Boolean circuits in generating uniform symmetric distributions. Let $f:\{0,1\}^m \rightarrow \{0,1\}^n$ be a Boolean function where each output bit of $f$ depends only on $O(1)$ input bits. Assume the output distribution of $f$ on uniform input bits is close to a uniform distribution $D$ with a symmetric support. We show that $D$ is essentially one of the following six possibilities: (1) point distribution on $0^n$, (2) point distribution on $1^n$, (3) uniform over $\{0^n,1^n\}$, (4) uniform over strings with even Hamming weights, (5) uniform over strings with odd Hamming weights, and (6) uniform over all strings. This confirms a conjecture of Filmus, Leigh, Riazanov, and Sokolov (RANDOM 2023). |
|
9:00am to 9:50am - Zoom - Inverse Problems Youssef Marzouk - (MIT) Dimension reduction in nonlinear Bayesian inverse problems |
|
1:00pm to 1:50pm - RH 510R - Algebra Manny Reyes - (UCI) Localization in noncommutative rings and categories To construct derived categories in the coming weeks, we will want to localize a category of complexes at a certain set of morphisms. What does it mean to localize a category? This is related to the older question of what it means to localize a noncommutative ring. I will survey the theory of Ore localization for rings, and point to the way that it generalizes to localizations of categories. |
|
3:00pm to 4:00pm - RH 306 - Number Theory Christian Klevdal - (UCSD) Periods and p-adic Hodge structures Complex Hodge theory equips the rational singular cohomology of smooth projective variety with a Hodge filtration, and period maps measure how these filtrations vary in families. Period maps are highly transcendental in nature, and the transcendence properties of these maps reflect interesting aspects of the geometry; for example a theorem of Cohen and Shiga-Wolfhart show that a complex abelian variety A has CM if and only both A and the Hodge filtration are defined over a number field. In this talk, we describe a similar situation in p-adic Hodge theory, and discuss joint work with Sean Howe that proves an analogue of the theorem of Cohen and Shiga-Wolfhart. The first part of the talk will contain a brief introduction to Hodge theory, so no previous experience with Hodge theory (complex or p-adic) is required! |
|
4:00pm to 5:00pm - RH 306 - Colloquium Francis Su - (Harvey Mudd) Sperner's Lemma: compelling proofs, generalizations, and applications Who doesn't like one of these three: geometry, topology, and combinatorics? Sperner's lemma, a combinatorial statement that is equivalent to the Brouwer fixed point theorem in topology, is amazing and powerful. I'll explain why, give heartwarming old and new proofs, and present some generalizations to polytopes that has surprised me with diverse applications: to the study of triangulations, to fair division problems, and the Game of Hex. |