There is a poster from the “Women in Math” club circulating around the internet. The poster displayed the pictures of four faculty members in our department. It was done by a club member with good intentions but with poor judgment. It was not meant to demean women or be satirical. We value women in mathematics and their contributions, and work to promote opportunities for women to succeed in mathematics.

# News Archive

## Statement on Women in Math

## Colloquium: Skyler Simmons (SUU)

**Title:** Stability of Collision-Based Periodic *n*-Body Problems

**Abstract:** The Newtonian n-body problem describes the motion of *n* point masses interacting with each other with gravitational force. The physical laws governing this motion were codified by Newton in his Principia in 1686. Under Newton’s laws, two colliding bodies’ velocities increase without bound as they approach collision. Levi-Civita demonstrated that through a suitable change of variables, certain collisions could be regularized, allowing the orbit to be continued past the collision. Variations on Levi-Civita’s work continue to be used in the study of collision-based orbits today. In this talk, I will present a few periodic orbits featuring collisions, describe the methods used to study their stability, and present known results about a few orbits.

**Date:** Thursday, February 22, 2018

**Time:** 4:00 PM

**Room:** 135 TMCB

## Colloquium: Robert Snellman (University of California San Diego)

**Title:** Special Values of *L*-functions and Fitting Ideals

**Abstract:** The Main Conjecture in Iwasawa theory provides a deep connection between a certain *p*-adic zeta function and arithmetic data associated to class groups in *p*-power cyclotomic extensions. Proved by Mazur and Wiles, later generalized and proved by Wiles for totally real fields, the Main Conjecture can be interpreted in terms of a Fitting ideal. I will give an overview of the importance of higher Fitting ideals in the structure theory of modules, and provide a conjecture giving a relationship between higher Fitting ideals of Iwasawa modules and special values of *L*-functions.

**Date:** Thursday, February 15, 2018

**Time**: 4:00 PM

**Room:** 135 TMCB

## Alumni Spotlight: Robert Luke Jr.

## Colloquium: Russell Ricks (Binghampton University)

**Title:** A Rank Rigidity Result for Certain Nonpositively Curved Spaces via Spherical Geometry

**Abstract:** To understand the geometry of nonpositively curved (NPC) spaces, it is natural to classify the various types of spaces that can occur. The Rank Rigidity Theorem for closed NPC manifolds separates the class of closed NPC manifolds into three very distinct types, and proves that nothing else can exist.

A version of Rank Rigidity has been conjectured for more general NPC spaces (CAT(0) spaces). In this talk, we discuss some progress toward the general conjecture, by reducing the problem to looking at patterns on spheres in the boundary at infinity. In particular, we can prove the conjecture for certain NPC spaces with one-dimensional boundary. In contrast to previous rank rigidity results, we do not assume any additional structure (such as a polyhedral or manifold structure) on the space.

Date: Tuesday, February 13

Time: 4:00 PM

Room: 135 TMCB

## Colloquium: Tuan Pham (University of Minnesota)

**Speaker:** Tuan Pham

**Title:** Minimal blowup data for potential Navier-Stokes singularities in the half space

**Abstract:** It is known that the mild solutions to the incompressible 3D Navier-Stokes Equations (NSE), either in the whole space or a smooth domain with nonslip boundary condition, exist locally in time. Provided that a blowup solution exists, then it has been shown that a so-called minimal blowup data for NSE in the whole space exists. In this talk, I will explain how the presence of the boundary might influence the existence of minimal blowup data. This is joint work with Vladimir Sverak. Our results are motivated by a theorem of Gregory Seregin on boundary regularity.

**Date:** Thursday, February 8, 2018

**Time**: 11:00 AM (NOTE SPECIAL TIME)

**Room:** 135 TMCB

## Winter Social

Come break the ice at the Math Student Winer Social. The party will be held at 6:30 PM on Friday, February 2nd 2018 in the Math Lab. Enjoy Pizza, Brownies, and Games!

## Colloquium: Dane Skabelund

**Title:** Algebraic Curves with Many Points over Finite Fields

**Abstract:** Algebraic curves with many points over finite fields have proven useful for creating good error-correcting codes and designing efficient algorithms for multiplication in finite fields. In this talk, I will discuss these applications, and describe the construction of two families of curves which meet the Hasse-Weil bound.

**Date and time:** Thursday, January 18 at 4:00 in room 135 TMCB.

## Colloquium: Domingo Toledo

**Title:** Inequalities in Topology Motivated by the Schwarz Lemma

**Abstract:** We will discuss a number of inequalities that can be stated in purely topological terms, but their proofs may involve other ideas. The protoptype is Knesers inequality for the degree of a map of Riemann surfaces, published in 1930: if *X*, *Y* are Riemann surfaces of genus (*g _{X},g_{Y}*) > 1 and

*f*:

*X*→

*Y*is a continuous map, then |

*degree*(

*f*)| ≤ (

*g*− 1)/(

_{X}*g*− 1). If

_{Y}*X*,

*Y*have complex structures and

*f*is holomorphic, then the inequality would be an immediate consequence of the Schwarz Lemma: holomorphic maps of the unit disk do not increase length in the Poincaré metric. We will discuss proofs of this inequality and related ones by various methods: bounded cohomology, harmonic maps, Higgs bundles. We will also indicate, as time permits, how these inequalities have motivated much work on the structure of the space of representations of the fundamental group of a surface in various Lie groups. This will be an exposition of work of Milnor, Wood, Dupont, Goldman, Gromov, Hitchin, and many others. It should be mentioned that some of the current work on this subject uses Ahlfors generalization of the Schwarz Lemma in a very essential way.

**Date and time:** Tuesday, January 16 at 4:00 in room 135 TMCB.

## Focus on Math: Dana Richards

The vast majority of mathematical puzzles ask for the existence of a solution. It is merely an exercise when the method is known and it is more of a puzzle when the method is not clear. An algorithmic puzzle takes this further by only asking for the method itself or a property of the method. It is in this sense that much of computer science is puzzle solving. We discuss the theory behind this in the context of material taken from Martin Gardner’s Scientific American column. The answer to the following puzzle will be given:

There are five pirates dividing up 100 gold coins. Pirates are strictly ordered by seniority, are very logical and wish to live. The rule pirates use to divide gold is: (1) the most senior pirate suggests a division, (2) all pirates vote on it, (3) if at least half vote for it then it is done, otherwise the senior pirate is killed and the process starts over. What happens?

Dana Richards is an associate professor of Computer Science at George Mason University. His research is on theoretical and algorithmic topics. He has been a friend of Martin Gardner for nearly four decades and has edited Gardner’s book

*The Colossal Book of Short Puzzles and Problem*s.

Join us at 4:00 on March 22nd to hear from Dana in 1170 TMCB.