Mohammed Abouzaid
Stanford University
Photo Credit: Stanford University
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AMS Invited Address
One Hundred Years of Morse Theory
Wednesday January 8, 2025, 2:10 p.m.-3:15 p.m.
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Maria-Florina Balcan
Carnegie Mellon University
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ASL Invited Address
Machine Learning Theory: New Challenges and Connections
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Anton Bernshteyn
UCLA
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ASL Invited Address
Some Recent Progress in Descriptive Combinatorics
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Tai-Danae Bradley
SandboxAQ
Photo credit: Jon Meadows
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NAM Claytor-Woodard Lecture
To be announced
Thursday, January 9, 2025: 2:10 p.m.-3:15 p.m.
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Semyon Dyatlov
MIT
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AMS Invited Address
Uncertainty Principles in Quantum Chaos
Saturday January 11, 2025, 3:20 p.m.-4:25 p.m.
In quantum mechanics, the pure states of a particle are the eigenfunctions of the associated quantum Hamiltonian. A commonly studied setting is that of compact Riemannian manifolds, where the pure quantum states are the eigenfunctions of the Laplace-Beltrami operator. The behavior of eigenfunctions in the high energy limit (i.e. with the eigenvalue going to infinity) is known to be connected to the dynamics of the geodesic flow on the manifold.
A fundamental problem in quantum chaos is to understand localization of eigenfunctions when the geodesic flow has chaotic behavior. This can be done using semiclassical measures, which are limiting objects on the cotangent bundle of the manifold capturing concentration of a high energy sequence of eigenfunctions in the position/frequency space. The Quantum Ergodicity theorem, going back to the 1970s--80s, states that most eigenfunctions equidistribute, that is, converge to the volume measure. The Quantum Unique Ergodicity (QUE) conjecture claims that the entire sequence of eigenfunctions equidistributes, that is the only semiclassical measure is the volume measure.
In this talk I will discuss two partial results towards the QUE conjecture. Each of these says that every semiclassical measure is delocalized: one is the statement that the measure has full support, and the other one is a lower bound on the entropy of the measure. I will highlight the role played in the proofs by uncertainty principles such as the Fractal Uncertainty Principle and the Entropic Uncertainty Principle.
Based on joint works with Jean Bourgain, Long Jin, St\'ephane Nonnenmacher, Jayadev Athreya, Nicholas Miller, and Alex Cohen.
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Joan Ferrini-Mundy
University of Maine
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TPSE Invited Address
Friday January 10, 2025, 8:30 a.m.-9:35 a.m.
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Wilfrid Gangbo
UCLA
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CRM-PIMS-AARMS Invited Address
Free Viscosity Solutions
Friday January 10, 2025, 9:40 a.m.-10:45 a.m.
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Alexi Block Gorman
Ohio State University
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ASL Invited Address
Characterizing Expansions of $R$ and $N$ by $k$-automatic sets
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Anne Greenbaum
University of Washington
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ILAS Invited Address
Are Iterative Linear System Solvers Backward Stable?
Thursday January 9, 2025, 9:40 a.m.-10:45 a.m.
This is a question that I often discuss with colleagues but we seldom come to a definitive conclusion. One reason is that “backward stability” is not precisely defined – it is defined in a number of different ways throughout the literature. Roughly, a backward stable algorithm for solving $Ax=b$, when implemented on a machine with unit roundoff $u$, produces a result $\hat{x}$ that satisfies $(A+\Delta A)\hat{x}=b+\Delta b$, where $\|\Delta A\|\leq \epsilon \|A\|$ and $\|\Delta b\|\leq \epsilon\| b\|$, where $\epsilon=p(n)u+O(u^2)$ and $p(n)$ is a polynomial in the problem size $n$. However, one must be careful to specify the domain of allowable matrices $A$, which may depend on $u$, as well as the details of the implementation. Additionally, for some iterative methods, there is a dependence on $k$, the number of steps for which the algorithm is run or, perhaps, a bound on the number of steps needed for a corresponding problem assuming exact arithmetic; thus we may need to replace $p(n)$ by $p(n, k)$.
In this talk, I will survey the literature on the attainable accuracy of iterative methods such as simple iteration (Jacobi, Gauss-Seidel, SOR, iterative refinement), steepest descent, and the conjugate gradient and Lanczos algorithms.
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Neena Gupta
Indian Statistical Institute
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AWM-AMS Noether Lecture
The Abhyankar-Sathaye Conjecture for Linear Hyperplanes
Thursday January 9, 2025, 3:20 p.m.-4:25 p.m.
In a famous survey paper published in 1996, H. Kraft compiled a list of eight challenging problems on affine $n$-spaces, including the Zariski Cancellation Problem (ZCP), the Embedding Problem and the Linearisation Problem.
The ZCP, which asks whether the affine $n$-space is cancellative, has an affirmation solution for $n=1$ and $n=2$ and the speaker had shown that in positive characteristic, the affine $n$-space is not cancellative when $n>2$.
In characteristic zero, the Embedding Problem has an affirmative solution when $n=2$; it is the famous Epimorphism Theorem of Abhyankar-Moh and Suzuki. The Abhyankar-Sathaye Conjecture, a special case of the Embedding Problem, asserts that any embedding of the affine $n-1$-space in affine $n$-space is rectifiable for any integer $n \ge 3$. The problem is open in general. When $n=3$, any linear plane was shown to be a coordinate by A. Sathaye (in characteristic zero) and P. Russell (in general).
In recent decades some of the central problems on affine spaces crucially involved the settling of questions of the type:
(i) whether a specified linear polynomial $H$ in $k[X_1, \dots, X_n]$ is a hyperplane and
(ii) whether linear hyperplanes of a certain form are coordinates.
Problem (i) for certain specified linear polynomials defined by M. Koras and P. Russell was crucial for the Linearization Problem. Again, central to the speaker's researches around the ZCP was the settling of Problems (i) and (ii) for a generalized version of certain linear polynomials defined by T. Asanuma. Note that Problem (ii) is a special case of the Abhyankar-Sathaye Conjecture.
In this talk we shall present certain new families of linear hyperplanes where the Abhyankar-Sathaye Conjecture holds. They arose from joint works with Parnashree Ghosh and Ananya Pal.
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Pamela Harris
University of Wisconsin-Milwaukee
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AMS Lecture on Education
Saturday January 11, 2025, 9:40 a.m.-10:45 a.m.
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Eric Hsu
San Francisco State University
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MAA Lecture on Teaching & Learning
Thursday January 9, 2025, 10:50 a.m.-11:55 a.m.
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Svetlana Jitomirskaya
University of California Berkeley
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AMS Colloquium Lectures: Lecture I
Wednesday January 8, 2025, 1:00 p.m. - 2:05 p.m.
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Svetlana Jitomirskaya
University of California Berkeley
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AMS Colloquium Lectures: Lecture II
Thursday January 9, 2025, 1:00 p.m. - 2:05 p.m.
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Svetlana Jitomirskaya
University of California Berkeley
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AMS Colloquium Lectures: Lecture III
Friday January 10, 2025, 1:00 p.m. - 2:05 p.m.
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Rajesh Kasturirangan
Socratus Foundation
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SIGMAA on the Philosophy of Mathematics Guest Speaker
Friday January 10, 2025, 5:45 p.m.-6:45 p.m.
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Kristin Lauter
Meta
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AMS Erdős Lecture for Students
Wednesday January 8, 2025, 10:50 a.m.-11:55 a.m.
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Yann LeCun
Meta
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AMS Josiah Willard Gibbs Lecture
Thursday January 9, 2025, 5:00 p.m.-6:00 p.m.
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Steven Lee
Department of Education Office of Science
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SIAM Invited Address
Friday January 10, 2025, 11:00 a.m.-12:05 p.m.
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Lester Mackey
Stanford University
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AMS John von Neumann Lecture
Advances in Distribution Compression
Wednesday January 8, 2025, 9:40 a.m.-10:45 a.m.
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Victor Moll
Tulane University
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MAA-SIAM-AMS Hrabowski-Gates-Tapia-McBay Lecture
Integral tales: Some Unexpected Connections
Friday January 10, 2025, 9:00 a.m.-10:00 a.m.
During the process of learning Calculus one observes that there is a well-defined list of rules to compute derivatives: product, quotient and chain rules are among the first taught in every class. On the other hand, when one tries to compute integrals, the student is left with a feeling that now there is simply a collection of tricks. There is no clear reason of why one can integrate $e^{x}$ is a simple manner, but the integral of $e^{x^{2}}$ is more complicated. One learns these tricks from the instructor, by talking to older classmates or by searching for them online. At the end, there seems to be no systematic way of doing this.
It is remarkable that, in the search of producing closed-forms of definite integrals, one finds many interesting connections with apparently disjoint parts of Mathematics. Examples will include $(1)$ properties of a collection of positive integers appearing in the evaluation of a rational functions, $(2)$ a planar dynamical system connected with a variation of the arithmetic-geometric mean and $(3)$ a list of definite integrals involving the gamma function.
The lecture will be suitable for undergraduates and it will include stories about how the speaker got involved in such projects.
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Emma Murphy
University of Toronto
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Spectra Lavender Lecture
Thursday January 9, 2025, 2:10 p.m.-3:15 p.m.
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Theodore A. Slaman
University of California, Berkeley
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ASL Invited Address
Extending Borel's Conjecture from Measure to Dimension
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Daniel Turetsky
Victoria University of Wellington
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ASL Invited Address
True Stages for Computability and Effective Descriptive Set Theory
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Ravi Vakil
Stanford University
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MAA-AMS-SIAM Gerald and Judith Porter Public Lecture
Saturday January 11, 2025, 2:15 p.m.-3:20 p.m.
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Kirsten Wickelgren
Duke University
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AMS Invited Address
Arithmetic Aspects of Enumerative Geometry
Friday January 10, 2025, 2:10 p.m.-3:15 p.m.
Enumerative geometry answers questions such as "How many lines meet four lines in space?" and "how many conics pass through 8 general points of the plane?" Fixed answers to such questions (here, 2 and 12) are obtained by working over an algebraically closed field like the complex numbers. Some of the solutions may be real, or integral, or defined over Q[i], but the fixed count does not see the difference. Homotopy theory on the other hand, studies continuous deformations of maps. In its modern form, it provides a framework to study shape in more algebraic and analytic contexts. This talk will introduce some interactions of homotopy theory with the arithmetic of solutions to enumerative problems in geometry. The study of such interactions was initiated in joint work with Jesse Kass and independently by Marc Hoyois and Marc Levine.
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Rebecca Willett
University of Chicago
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AAAS-AMS Invited Address
To be announced
Friday January 10, 2025, 10:50-11:55 a.m.
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Daniela Witten
University of Washington
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PME J. Sutherland Frame Lecture
Selective Inference for Real-World Problems
Thursday January 9, 2025, 9:40 a.m.-10:45 a.m.
Statistics courses suppose an idealized version of the scientific process, in which a researcher is faced with a specific scientific question, which they then formulate as a statistical null hypothesis. The researcher then (i) collects data to test this null hypothesis, (ii) either rejects or fails to reject the null hypothesis, and then (iii) publishes the result (or not).
However, real life often proceeds quite differently. Data are often collected at massive scale before a specific scientific question is ever asked; in fact, often the goal of data collection is to explore the data in order to identify interesting scientific questions, and then to answer those questions based on the same data. Unfortunately, if the null hypothesis tested is a function of the data (rather than having been specified in advance), then the hypothesis tests, confidence intervals, and other measures of uncertainty taught in our statistics courses will not be valid.
Selective inference is a relatively new subfield of statistics aimed at bridging the aforementioned gap between the idealized version of the scientific process, and the actual way that science is conducted. In a nutshell, the philosophy behind selective inference is as follows: to test a null hypothesis generated from the data, we must account for the fact that the data led us to generate this particular null hypothesis. We will discuss a number of approaches for selective inference, ranging from the simple (sample splitting) to the more complex (conditional selective inference).
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Alexander Wright
University of Michigan
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AMS Maryam Mirzakhani Lecture
Friday January 10, 2025, 3:20 p.m.-4:25 p.m.
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Jinhe Ye
University of Oxford
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ASL Invited Address
Lang-Weil Estimate in Finite Difference Fields
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Andy Zucker
University of Waterloo
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ASL Invited Address
Topological Dynamics and Continuous Logic
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