Maryanth Malliaris
Distinguished Professor of Mathematics
University of Chicago

Cardinal Invariants of the continuum allow mathematicians to investigate properties of the (undecidable) continuum hypothesis. In this lecture, we will start from the beginning and explore some of this world, including some surprising interactions with model theory.

Biography of Dr. Malliaris

Dr. Maryanthe Malliaris is a professor of mathematics at the University of Chicago, specializing in model theory, set theory, and topology. She earned her PhD in 2009 from UC Berkeley, where she studied under Thomas Scanlon. Her research includes significant contributions to unstable model theory and set theory, including her work with Saharon Shelah on the equality of two cardinal characteristics of the continuum.

Dr. Malliaris has received several honors, including the Kurt Gödel Research Prize in 2010 and the Hausdorff Medal in 2017. She has also been an invited speaker at the International Congress of Mathematicians. Her work is widely recognized in the mathematical community.

Professor Isabel Vogt
April 13th, 4 pm, Etcheverry 3106
Associate Professor of Mathematics
Brown University

The interpolation problem is one of the oldest in mathematics. In its most broad form it asks: when can a curve of a given type be passed through a given number of points? We will consider curves that are described by polynomial equations. Because polynomial equations are ubiquitous in mathematics and the sciences more generally, such curves appear in many different contexts. The interpolation problem, in particular, has real-world applications to cryptography and information transfer. In this talk, I'll survey work on the interpolation problem from Euclid to the modern day, ending with recent joint work of mine with Eric Larson. No prerequisites will be assumed.

Biography of Professor Vogt

Isabel Vogt is a mathematician who works on algebraic geometry and number theory. She has published several papers on topics such as isolated and parametrized points on curves, conic bundle threefolds, Brauer classes, and Hurwitz-Brill-Noether theory. Her research is in the intersection of algebraic geometry and number theory, including the geometry of algebraic curves and rational and low degree points on varieties.

In 2022, she and her husband Eric Larson solved the interpolation problem for algebraic curves, which was a longstanding question in mathematics concerning how many random points certain types of curves can pass through in high-dimensional spaces.

She is currently an associate professor at Brown University, and she received her PhD in June 2019 from MIT, where she was a student of Bjorn Poonen and Joe Harris. She has in the past worked with Ravi Vakil at Stanford University, working with Ravi Vakil and as an assistant professor at the University of Washington.

Vogt adheres to Federico Ardila's axioms, emphasizing that mathematical potential is universally distributed, everyone can have empowering mathematical experiences, mathematics is a versatile tool shaped by diverse communities, and every student deserves dignity and respect.

Priyam Patel
University of Utah

Emily Riehl
Johns Hopkins University

Kelli Talaska
UC Berkeley
Co-hosted with WiM (now GEM)

Laura Starkston
UC Davis

Dr. Kristin Lauter
Microsoft Research

This talk will give an overview of the history of various hard problems in number theory which are used as the basis for cryptosystems. I will survey the evolution of attacks and discuss the upcoming NIST competition to standardize new cryptographic schemes for a post-quantum world. I will present some current proposals for post-quantum systems based on supersingular isogeny graphs of elliptic curves and lattice-based cryptosystems in cyclotomic number fields. Supersingular Isogeny Graphs were proposed for use in Cryptography in 2006 by Charles-Goren-Lauter, and are currently being considered as candidates for standardization in several tracks of the 2017 NIST Post-Quantum Cryptography International Competition. These are Ramanujan graphs whose nodes are supersingular elliptic curves and edges are isogenies between them.

Biography of Dr. Lautner

Kristin Estella Lauter is a mathematician and cryptographer whose research areas are number theory, algebraic geometry, and applications to cryptography. She is particularly known for her work on homomorphic encryption, elliptic curve cryptography, and for introducing supersingular isogeny graphs as a hard problem into cryptography. She is a Principal Researcher and Research Manager of the Cryptography Group at Microsoft Research in Redmond, Washington. She served as President of the Association for Women in Mathematics from 2015 –2017.  She has published more than 100 papers and holds more than 50 patents.

In 2008 Lauter and her coauthors were awarded the Selfridge Prize in Computational Number Theory.  She was elected to the 2015 Class of Fellows of the American Mathematical Society "for contributions to arithmetic geometry and cryptography as well as service to the community."  In 2017, she was selected as a fellow of the Association for Women in Mathematics in the inaugural class, and as the 2018-2020 Polya Lecturer for the Mathematical Association of America.

Lauter received her BA, MS, and Ph.D degrees in mathematics from the University of Chicago, in 1990, 1991, and 1996, respectively. Prior to joining Microsoft, she held positions as a visiting scholar at Max Planck Institut fur Mathematik in Bonn, Germany (1997), T.H. Hildebrandt Research Assistant Professor at the University of Michigan (1996-1999), and a visiting researcher at Institut de Mathematiques Luminy in France (1999).

She is a co-founder of the Women in Numbers Network, a research collaboration community for women in number theory, and she is the lead PI for the AWM NSF Advance Grant (2015-2020) to create and sustain research networks for women in all areas of mathematics. She serves on the Board of Trustees of MSRI, the Advisory Board of the Banff International Research Station and has served on the Council^[7] of the American Mathematical Society (2014-2017).

Elena Fuchs
Assistant Professor of Mathematics
UC Davis

In the early 70’s, the concept of “expander graphs” was introduced as an optimal model for networks of arbitrary size. Back then, it was not even known whether such graphs exist or not. Today, we not only know that they exist, but have seen their importance come up in a great spectrum of fields in mathematics and computer science. In this talk, we will explore what these graphs are and give an idea about how they have recently made a splash on the number theory scene. No prerequisites are required.

Biography of Prof. Fuchs

Professor Elena Fuchs received her B.A. in mathematics here at UC Berkeley in 2005 and earned her Ph.D. in number theory from Princeton University before beginning postdoctoral work at the Institute for Advanced Study in 2010. Since then, she has held positions at UC Berkeley and University of Illinois, Urbana-Champaign. In 2016, Professor Fuchs was awarded the Sloan Fellowship for early-career researchers and is currently an assistant professor at UC Davis.

A committee member of the Association for Women in Mathematics, Professor Fuchs was the president of Princeton University Noetherian Ring and co-founded Princeton Math Circle as a graduate student. Since then, she has been involved in various events including a Summer Workshop for Women in Mathematics at Princeton, Illinois Number Theory Conference, and the 2016 Midwestern Women in Mathematics Symposium as a co-organizer.

Professor Fuchs does research on the interplay between geometric group theory and number theory, such as Apollonian gaskets, which are fractals made of circles. In particular, she is interested in arithmetic properties of integer matrix groups such as various monodromy groups and hyperbolic reflection groups.