Special Lecture Archives for Fall 2022 to Spring 2023
Emergent behaviors in adaptive dynamical networks with applications to biological and social systems
When: Mon, July 12, 2021 - 2:00pmWhere: https://umd.zoom.us/j/91277872841?pwd=L25BWFJwMC9uLzJKR1JiY3d0Y3B4QT09
Speaker: Brandon Alexander (UMD - AMSC) -
Fokker-Planck Equations and Machine Learning
When: Tue, November 30, 2021 - 4:00pmWhere: https://umd.zoom.us/j/6997828301
Speaker: Yuhua Zhu (Stanford University) - https://www.yuhuazhu.org/
Abstract: As the continuous limit of many discretized algorithms, PDEs can provide a qualitative description of algorithm's behavior and give principled theoretical insight into many mysteries in machine learning. In this talk, I will give a theoretical interpretation of several machine learning algorithms using Fokker-Planck (FP) equations. In the first one, we provide a mathematically rigorous explanation of why resampling outperforms reweighting in correcting biased data when stochastic gradient-type algorithms are used in training. In the second one, we propose a new method to alleviate the double sampling problem in model-free reinforcement learning, where the FP equation is used to do error analysis for the algorithm. In the last one, inspired by an interactive particle system whose mean-field limit is a non-linear FP equation, we develop an efficient gradient-free method that finds the global minimum exponentially fast.
Non-Parametric Estimation of Manifolds from Noisy Data
When: Wed, December 1, 2021 - 4:30pmWhere: https://umd.zoom.us/j/6997828301
Speaker: Yariv Aizenbud (Yale University) - https://gauss.math.yale.edu/~ya248/
Abstract: A common task in many data-driven applications is to find a low dimensional manifold that describes the data accurately. Estimating a manifold from noisy samples has proven to be a challenging task. Indeed, even after decades of research, there is no (computationally tractable) algorithm that accurately estimates a manifold from noisy samples with a constant level of noise.
In this talk, we will present a method that estimates a manifold and its tangent in the ambient space. Moreover, we establish rigorous convergence rates, which are essentially as good as existing convergence rates for function estimation.
Statistical Learning and Matching Markets
When: Thu, December 2, 2021 - 4:00pmWhere: https://umd.zoom.us/j/6997828301
Speaker: Xiaowu Dai (UC-Berkeley) - https://www.xiaowudai.org/
Abstract: We study the problem of decision-making in the setting of a scarcity of shared resources when the preferences of agents are unknown a priori and must be learned from data. Taking the two-sided matching market as a running example, we focus on the decentralized setting, where agents do not share their learned preferences with a central authority. Our approach is based on the representation of preferences in a reproducing kernel Hilbert space, and a learning algorithm for preferences that accounts for uncertainty due to the competition among the agents in the market. Under regularity conditions, we show that our estimator of preferences converges at a minimax optimal rate. Given this result, we derive optimal strategies that maximize agents' expected payoffs and we calibrate the uncertain state by taking opportunity costs into account. We also derive an incentive-compatibility property and show that the outcome from the learned strategies has a stability property. Finally, we prove a fairness property that asserts that there exists no justified envy according to the learned strategies. This is a joint work with Michael I. Jordan.
TBA
When: Fri, December 3, 2021 - 3:15pmWhere: https://umd.zoom.us/j/6997828301
Speaker: Miklos Racz (Princeton University) - https://mracz.princeton.edu/
Surface phenomena in the 2D and 3D Ising model
When: Mon, December 6, 2021 - 4:00pmWhere: https://umd.zoom.us/j/6997828301
Speaker: Reza Gheissari (UC-Berkeley) - https://www.stat.berkeley.edu/~gheissari/
Abstract: Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two
thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface
phenomena and universality classes emerge.
On the structure of translational tilings
When: Tue, December 7, 2021 - 4:30pmWhere: https://umd.zoom.us/j/6997828301
Speaker: Rachel Greenfeld (UCLA) - https://www.math.ucla.edu/~greenfeld/
Abstract: Given a finite collection of bounded subsets of an additive group, can we decide whether it is possible to tile the group by translated copies of them? Suppose that they do tile the group, what can be said about the structure of the tiling? These questions are closely related. In the talk, we will discuss this relation, survey the study of translational tilings and present some applications and connections to other interesting problems.
Reciprocity laws from quadratic reciprocity to genus 2 curves
When: Wed, December 8, 2021 - 11:10amWhere: https://umd.zoom.us/j/6997828301
Speaker: George Boxer (Orsay) -
Abstract: I will survey reciprocity laws in number theory and the Langlands program starting with Gauss’s law of quadratic reciprocity and ending with my recent work on (potential) modularity of genus 2 curves with Calegari, Gee, and Pilloni. No background in number theory will be assumed.
Turbulent Weak Solutions of the 3D Euler Equations
When: Fri, December 10, 2021 - 3:15pmWhere: https://umd.zoom.us/j/6997828301
Speaker: Matthew Novack (IAS) - https://sites.google.com/view/mnovackmath/home
Abstract: The Navier-Stokes and Euler equations are the fundamental models for describing viscous and inviscid fluids, respectively. Based on ideas which date back to Kolmogorov and Onsager, solutions to these equations are expected to dissipate energy, which in turn suggests that such solutions are somewhat rough and thus only weak solutions. At these low regularity levels, however, one may construct will weak solutions using convex integration methods. In this talk, I will discuss the motivation and methodology behind joint work with Tristan Buckmaster, Nader Masmoudi, and Vlad Vicol in which we construct wild solutions to the Euler equations which deviate from the predictions of Kolmogorov's classical K41 phenomenological theory of turbulence.
Canonical metrics and stability of Fano varieties
When: Mon, December 13, 2021 - 4:00pmWhere: https://umd.zoom.us/j/6997828301
Speaker: Ziquan Zhuang (MIT) - https://sites.google.com/view/ziquan-zhuang/
Abstract: Finding canonical metrics, especially Kaehler-Einstein metrics, on compact Kaehler varieties has been an intense topic of research for decades. A famous result of Yau says that every compact Kaehler manifold with non-positive first Chern class admits a Kaehler-Einstein metric (when the Chern class is negative this was also independently proved by Aubin). In this talk, I'll present some recent joint works with Hamid Abban, Yuchen Liu and Chenyang Xu on the existence of Kaehler-Einstein metrics when the first Chern class is positive and the variety is possibly singular (such varieties are called Fano varieties). I'll focus on two particular aspects: the solution of the Yau-Tian-Donaldson conjecture, which predicts that the existence of Kaehler-Einstein metrics on Fano varieties is equivalent to an algebro-geometric stability condition called K-polystability, and a systematic approach (using birational geometry) to decide whether Kaehler-Einstein metrics exist on explicit Fano varieties.
Deep learning-based enhancements in numerical analysis
When: Tue, December 14, 2021 - 4:00pmWhere: https://umd.zoom.us/j/6997828301
Speaker: Deep Ray (USC) - https://deepray.github.io/
Abstract: Mathematically-sound numerical algorithms in computational physics have been developed and iteratively improved over the last few decades. These include methods to solve partial differential equations, inverse-problems, and quantifying uncertainty in observed dynamics. However, many of these algorithms suffer from bottlenecks that manifest in the form of computationally expensive sub-components, or problem-dependent parameters that require empirical tuning. In this talk, I will present novel data-driven approaches to overcome such bottlenecks. In particular, I will demonstrate how deep neural networks can be trained to assist and improve numerical methods. This includes the detection and control of spurious Gibbs oscillations encountered while using high-order methods to approximate solutions with low-regularity, approximation of parameter- to-output maps in many-query problems, and the representation of high-dimensional priors in Bayesian inference.
Borel-definable Algebraic Topology
When: Wed, December 15, 2021 - 4:00pmWhere: https://umd.zoom.us/j/6997828301
Speaker: Martino Lupini (Victoria University, Wellington) - https://people.wgtn.ac.nz/martino.lupini
Abstract: In this talk, I will explain how ideas and methods from logic can be used to obtain refinements of classical invariants from homological algebra and algebraic topology. I will then present some applications to classification problems in topology. This is joint work with Jeffrey Bergfalk and Aristotelis Panagiotopoulos.
Strongly-Disordered Topological Insulators
When: Thu, December 16, 2021 - 4:00pmWhere: https://umd.zoom.us/j/6997828301
Speaker: Jacob Shapiro (Princeton University) - https://physics.princeton.edu//~js129/
Abstract: Topological insulators are novel materials which insulate in their bulk, yet, along their boundary are excellent conductors. Their exotic properties are explored by identifying the topological space of quantum mechanical Hamiltonians and calculating its set of path-connected components, which in interesting cases, has more than one component. The components induce a topological invariant which corresponds to an experimentally measurable physical quantity. I will focus on such systems in the regime of strong disorder, which is of particular physical relevance, and leads to rich problems in analysis and probability.
Some Recent Results On Wave Turbulence: Derivation, Analysis, Numerics and Physical Application
When: Wed, January 19, 2022 - 3:15pmWhere: https://umd.zoom.us/j/6997828301
Speaker: Minh-Binh Tran (Southern Methodist University) -
Abstract: Wave turbulence describes the dynamics of both classical and non-classical nonlinear waves out of thermal equilibrium. Recent mathematical interests on wave turbulence theory have their roots from the works of Bourgain, Staffilani and Colliander-Keel-Staffilani-Takaoka-Tao. In this talk, I will present some of our recent results on wave turbulence theory. In the first part of the talk, I will discuss our rigorous derivation of wave turbulence equations. The second part of the talk is devoted to the analysis of wave turbulence equations as well as some numerical illustrations. The last part concerns some physical applications of wave turbulence theory. The talk is based on my joint work with Staffilani (MIT), Soffer (Rutgers), Pomeau (ENS Paris), and Walton (PhD student at SMU).
Discretization-Invariant Operator Learning: Algorithms and Theory
When: Thu, January 20, 2022 - 3:15pmWhere: https://umd.zoom.us/j/6997828301
Speaker: Haizhao Yang (Purdue University) -
Abstract: Learning operators between infinitely dimensional spaces is an important learning task arising in wide applications in machine learning, data science, mathematical modeling and simulations, etc. This talk introduces a new discretization-invariant operator learning approach based on data-driven kernels for sparsity via deep learning. Compared to existing methods, our approach achieves attractive accuracy in solving forward and inverse problems, prediction problems, and signal processing problems with zero-shot generalization, i.e., networks trained with a fixed data structure can be applied to heterogeneous data structures without expensive re-training. Under mild conditions, quantitative generalization error will be provided to understand discretization-invariant operator learning.
Singularities and nonuniqueness in fluids: the good, the bad and the ugly
When: Fri, January 28, 2022 - 3:15pmWhere: Kirwan Hall 3206
Speaker: Tristan Buckmaster (Princeton University) -
Abstract: In this talk, I will provide an overview of a broad spectrum of results related to both compressible and incompressible fluid flow. In the context of compressible flow, I will cover results related to shock waves and implosion. In the context of incompressible flow, I will survey results related to anomalous dissipation and non-uniqueness. I will attempt to tie all these results to fundamental problems in the field of mathematical fluid dynamics.
Recent progress on Chowla's conjecture
When: Wed, February 9, 2022 - 3:15pmWhere: Kirwan Hall 3206
Speaker: Maksym Radziwill (CalTech) -
Abstract: I will describe recent progress on our understanding of the factorization
of the integers, specifically consecutive integers. The main theme is the tension
between the additive and multiplicative structure of the integers. This is a central
topic in number theory, connected among others to problems of equidistribution
of arithmetic objects (subconvexity) or more classical problems such as the twin
prime conjecture (parity obstruction).
The first significant result towards Chowla's conjecture goes back to my work
with Matomaki from 2015. In the last six years this particular sub-area gave rise to
several new ideas in analytic number theory, specifically ideas related to entropy,
expander graphs and additive combinatorics. Among the recent achievements
are results on local Fourier uniformity and expansion in thin graphs connected
with prime divisors of integers.
In turn progress on this basic question gave back various results beyond number
theory in areas as distinct as combinatorics (Erdos discrepancy problem), mathematical
physics (spacing betweens eigenfunctions of the Laplacian on generic rectangular tori),
cryptography (smooth numbers in short intervals), ergodic theory (Sarnak's conjecture), etc.
I will discuss various papers joint with Matomaki, Helfgott, Ziegler, Tao and Teravainen and
also progress by others, e.g Tao, Walsh, Frantzikinakis and Host.
Inference for a large directed graphical model with interventions
When: Wed, March 9, 2022 - 3:15pmWhere: Kirwan Hall 3206
Speaker: Xiaotong Shen (University of Minnesota) -
Abstract: A directed graphical model has been widely used for causal discovery in the machine learning literature. Yet, inference for such a model has been largely unexplored. In this presentation, I focus on a directed graphical model with interventions. First, we propose constrained regressions for causal discovery to identify the ancestral relations in addition to the instrument interventions for each hypothesis-specific primary variable. On this ground, we derive modified likelihood ratio tests, eliminating nuisance parameters for hypothesis testing. To account for the uncertainty of causal discovery, we develop perturbation likelihood ratio tests by perturbing original data. Also, we show that the proposed tests achieve desired statistical properties. Finally, I will use numerical examples to demonstrate the effectiveness of the proposed methods.
This work is joint with Chunlin Li and Wei Pan at the University of Minnesota.
Reference: arXiv:2110.03805.
Missing Data Worksop
When: Wed, March 30, 2022 - 8:00amWhere: Kirwan Hall 3206
Speaker: Several speakers: Rod Little, Kim Jae-Kwang, Partha Lahiri, Rebecca Andridge (U. Michigan, Iowa State U., UMD, OSU) -
Abstract: Missing data is an important area of statistics. The workshop will feature well known experts who will give several lectures including an introduction and research work.
Quantum Computation and Cryptography: a changing landscape
When: Mon, April 4, 2022 - 2:00pmWhere: Zoom
Speaker: Andrea Coladangelo (UC Berkeley) - https://www.andreacoladangelo.com/
Abstract: Quantum computers will reshape the landscape of cryptography. On the one hand, they threaten the security of most modern cryptosystems. On the other, they offer fundamentally new ways to realize tasks that were never before thought to be possible. Crucially, cryptography is also a powerful lens through which to understand quantum computation. In this talk, I will explore the interplay between quantum computation and cryptography, and the many exciting questions at this intersection. I will describe examples that leverage quantum computers to protect against coercion in online elections, and to prevent piracy of software.
https://umd.zoom.us/j/98095131895?pwd=bFRySUJZSytQcjFVVis0dFpuWU1TZz09
In Praise of Not Paying Attention
When: Tue, April 19, 2022 - 4:30pmWhere: Kirwan Hall 3206
Speaker: Barry Cipra () -
Abstract: The speaker will describe some mathematical puzzles, problems, and games he has dreamt up over the years while letting his mind wander during math lectures and other occasions. If all goes well, the audience will find it a stimulating presentation…