# Michler Lecture Series

The Ruth I. Michler Memorial Prize of the AWM is awarded annually to a woman recently promoted to associate professor or an equivalent position in the mathematical sciences. The prize provides a fellowship for the awardee and enables her to focus on her research in the stimulating environment of the Cornell University Department during a semester that is free from teaching obligations. Recently promoted associate professors face many challenges as they prepare to take on greater leadership in research and in the profession. The Ruth I. Michler Memorial Prize honors outstanding women at this stage of their careers. Each year, the Michler Fellow is invited to give a lecture to an audience of faculty and graduate students.

# Upcoming Lectures

There will be two Michler Lectures on September 8th and September 22nd, 2022.

**Speakers:****September 8th (Online) - Anna Skripka, Michler Scholar**

Join Zoom Meeting at 4:00 p.m. - https://cornell.zoom.us/j/99398058613?pwd=MWhUci96N1lEMHBEMmJnVEtNdGIrQT09

Title: Untangling noncommutativity with operator integrals

Abstract: Operator integration is a collection of powerful methods and techniques that enable analysis of functions with noncommuting arguments. Such functions arise, in particular, in various problems of matrix analysis, mathematical physics, noncommutative geometry, and statistical estimation. Theory underlying multilinear operator integration has been developing for some seventy years, and by now has accumulated many deep results and important applications. I will give a flavor of subject and present several recent advancements.**September 22nd - Emily Witt, Michler Scholar**

This lecture will be in-person in 532 Malott Hall starting at 4:00 p.m.

Title: Local cohomology: An algebraic tool capturing geometric data

Abstract: Introduced by Grothendieck, the notion of local cohomology is defined in a purely algebraic way. However, it also encodes fundamental geometric and topological data. For instance, local cohomology can help determine the number of equations needed to define a variety, or how the irreducible components of a ring's spectrum fit together topologically.

Unfortunately, local cohomology modules can be huge-i.e., they are typically not finitely generated, and the data they carry can be hard to access. It can even be difficult to determine whether a given local cohomology module is zero!

In this talk, aimed toward a general audience, we discuss methods developed to better understand local cohomology, which involve rings of differential operators, invariant theory, and graph theory. We also describe recently discovered connections between local cohomology and geometry/topology.**Reception**

A joint reception for both Michler Fellows will be held in 532 Malott Hall from 3:30 - 4:00 p.m. on September 22nd.

Please contact Heather Peterson if you need accommodations.

**PREVIOUS LECTURE SERIES:**

**November 4, 2021**

Reception at 3:30 in 532 Malott Hall - Due to recent Covid guidelines the reception is open to the Cornell Math Department/Cornell Community only.

Presentation/Lecture at 4:00 - 5:00 in 251 Malott Hall - Hybrid format

Speaker: Shabnam Akhtari, Michler Scholar, University of Oregon and Cornell

Title: Representation of integers by binary forms

Abstract: Let F(x , y) be a binary form with integer coefficients and degree at least 3. Suppose F(x , y) is irreducible over the rational numbers. In 1909, Thue proved that for any given integer m, the equation F(x , y) = m has at most finitely many solutions in integers x and y. These equations are called Thue equations. We will explore some general questions: how many solutions can a Thue equation have? how often do Thue equations have any solution? We will also talk about applications of Thue equations in counting some interesting arithmetic objects, such as orders in number fields.

**October 18, 2018**

**Julie Bergner** of The University of Virginia

Reception at 3:30pm, 532 Malott Hall

If you need any special accommodations (e.g., dietary constraints, mobility constraints, etc.), please contact Heather Peterson, hko1@cornell.edu.

Lecture begins at 4:00pm, 532 Malott Hall

**Title: 2-Segal structures and the Waldhausen S-construction**

**Abstract:** The structure of a 2-Segal space was defined by Dyckerhoff and Kapranov and independently by Galvez-Carrillo, Kock, and Tonks under the name of decomposition space. Both groups found many examples in algebra, topology, and combinatorics, yet a common one was the output of Waldhausen's S-construction when applied to an exact category. In joint work with Osorno, Ozornova, Rovelli, and Scheimbauer, we give a more general version of this construction so that every 2-Segal space arises from it.

**Julia Gordon,**the University of British Columbia*Wilkie's theorem and (ineffective) uniform bounds*(November 2017)**Pallavi Dani**, Louisiana State University*Large-scale geometry of right-angled Coxeter groups*(March 2017)**Malabika Pramanik**, University of British Columbia*Needles, Bushes, Hairbrushes, and Polynomials*(October 2015)**Sema Salur**, University of Rochester*Manifolds with G2 structure and beyond*(March 2015)**Megumi Harada**, McMaster University*Newton-Okounkov bodies and integrable systems*(March 2015)**Ling Long**, Iowa State University*Atkin and Swinnerton-Dyer Congruences*(October 2012)**Anna Mazzucato**, Pennsylvania State University*The Analysis of Incompressible Fluids at High Reynolds Numbers*(March 2012)**Patricia Hersh**, North Carolina State University*Regular CS Complexes, Total Positivity and Bruhat Order*(November 2010)**Maria Gordina**, University of Connecticut*Lie's Third Theorem in Infinite Dimensions*(April 2010)**Irina Mitrea**, University of Virginia*Boundary-Value Problems for Higher-Order Elliptic Operators*(October 2008)**Rebecca Goldin**, George Mason University*The Geometry of Polygons*(September 2007)