Invited Speakers - A Closer Look

picture of Mohammed Abouzaid

Mohammed Abouzaid
Stanford University
Photo Credit: Stanford University

AMS Invited Address

One Hundred Years of Morse Theory

Wednesday January 8, 2025, 2:10 p.m.-3:15 p.m.

Maria-Florina Balcan
Carnegie Mellon University

ASL Invited Address

Machine Learning Theory: New Challenges and Connections

Anton Bernshteyn

ASL Invited Address

Some Recent Progress in Descriptive Combinatorics

picture of Semyon Dyatlov

Semyon Dyatlov

AMS Invited Address

Uncertainty Principles in Quantum Chaos

Saturday January 11, 2025, 3:20 p.m.-4:25 p.m.

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Joan Ferrini-Mundy
University of Maine

TPSE Invited Address

Friday January 10, 2025, 8:30 a.m.-9:35 a.m.

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Wilfrid Gangbo

CRM-PIMS-AARMS Invited Address

Free Viscosity Solutions

Friday January 10, 2025, 9:40 a.m.-10:45 a.m.

Alexi Block Gorman
Ohio State University

ASL Invited Address

Characterizing Expansions of $R$ and $N$ by $k$-automatic sets

picture of Anne Greenbaum

Anne Greenbaum
University of Washington

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

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

AMS Lecture on Education

Saturday January 11, 2025, 9:40 a.m.-10:45 a.m.

Eric Hsu
San Francisco State University

MAA Lecture on Teaching & Learning

Thursday January 9, 2025, 10:50 a.m.-11:55 a.m.

Svetlana Jitomirskaya
University of California Berkeley

AMS Colloquium Lectures: Lecture I

Wednesday January 8, 2025, 1:00 p.m. - 2:05 p.m.

Svetlana Jitomirskaya
University of California Berkeley

AMS Colloquium Lectures: Lecture II

Thursday January 9, 2025, 1:00 p.m. - 2:05 p.m.

Svetlana Jitomirskaya
University of California Berkeley

AMS Colloquium Lectures: Lecture III

Friday January 10, 2025, 1:00 p.m. - 2:05 p.m.

Rajesh Kasturirangan
Socratus Foundation

SIGMAA on the Philosophy of Mathematics Guest Speaker

Friday January 10, 2025, 5:45 p.m.-6:45 p.m.

Kristin Lauter

AMS Erdős Lecture for Students

Wednesday January 8, 2025, 10:50 a.m.-11:55 a.m.

Yann LeCun

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

SIAM Invited Address

Friday January 10, 2025, 11:00 a.m.-12:05 p.m.

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Lester Mackey
Stanford University

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

MAA-SIAM-AMS Hrabowski-Gates-Tapia-McBay Lecture

Friday January 10, 2025, 9:00 a.m.-10:00 a.m.

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Emma Murphy
University of Toronto

Spectra Lavender Lecture

Thursday January 9, 2025, 2:10 p.m.-3:15 p.m.

Theodore A. Slaman
University of California, Berkeley

ASL Invited Address

Extending Borel's Conjecture from Measure to Dimension

Daniel Turetsky
Victoria University of Wellington

ASL Invited Address

True Stages for Computability and Effective Descriptive Set Theory

Ravi Vakil
Stanford University

MAA-AMS-SIAM Gerald and Judith Porter Public Lecture

Saturday January 11, 2025, 2:15 p.m.-3:20 p.m.

picture of Kirsten Wickelgren

Kirsten Wickelgren
Duke University

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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Daniela Witten
University of Washington

PME J. Sutherland Frame Lecture

Selective Inference for Real-World Problems

Thursday January 9, 2025, 9:40 a.m.-10:45 a.m.

Alexander Wright
University of Michigan

AMS Maryam Mirzakhani Lecture

Friday January 10, 2025, 3:20 p.m.-4:25 p.m.

Jinhe Ye
University of Oxford

ASL Invited Address

Lang-Weil Estimate in Finite Difference Fields

Andy Zucker
University of Waterloo

ASL Invited Address

Topological Dynamics and Continuous Logic