Date
 Speaker
 Title

April 9 
Ahmad Reza Haj Saeedi Sadegh 
A topological identification of Schwartz functions
(Show/hide abstract)


A Schwartz function on $\mathbb{R}^n$ is defined as a function whose derivatives are all rapidly decaying, i.e. $x^{\alpha}\partial^{\beta}f$ vanishes at infinity. There are wellknown analytical identifications of these functions, but there is also a less known topological identification of these functions, which I will be talking about.

April 2 
Stephen White 
Imaging in Random Media
(Show/hide abstract)


"Imaging" describes a broad array of inverse problems in the applied sciences. Fundamentally, this problem involves inverting solutions to the wave equation, a task which is computationally infeasible in practice. Further, in many situations such as geological imaging, the medium in which waves propagate is unknown and must be modelled as random. In this talk, I will outline the basic challenges, modelling approaches, and proposed solutions to this problem.

March 26 (Postponed) 
Gabrielle Scullard 
The lisogeny path problem
(Show/hide abstract)


Cryptosystems are protected by the assumption that certain numbertheoretic problems are hard. But with the advent of quantum computers and quantum algorithms, there is a need to develop cryptosystems based on even harder problems. We will discuss one such problem, based on finding certain maps between certain types of elliptic curves. If time permits, we will also discuss the quaternion algebra analogue of the lisogeny path problem.

March 12 
Caleb Springer 
Website building (HTML/CSS) (Show/hide abstract)


It is important for every graduate student to create a clear and professional website to make themselves known and contactable. Moreover, the website needs to created before it is needed so that the website can be found through Google! None of us are necessarily "experts" in website building, but we can help each other get started.

March 5 @ 1:30pm (Delayed start) 
Sergio Zamora Barrera 
Lower Semicontinuity of the Fundamental Group (Show/hide abstract)


A lower semicontinuous functional $f$ is (informally) one that satisfies the condition $f(lim (x_n)) \leq liminf ( f(x_n) )$ for any convergent sequence $x_n$. I will talk about how, when viewed from the right perspective (GromovHausdorff convergence in compact length spaces), the fundamental group is lower semicontinuous.

February 26 
Caitlin Lienkaemper 
Do the flat earthers have a point? An investigation using topological data analysis.
(Show/hide abstract)


While most of us believe the Earth to be a sphere, the writer Samuel Rowbotham proposed in the 1849 pamphlet Zetetic Astronomy that the Earth is instead a flat disk surrounded by a wall of ice. We investigate his claim using topological data analysis. In particular, we give an introduction to persistent homology, a technique for estimating the underlying structure of a metric space using the distances between points sampled from the space. We attempt to use persistent homology to compute the shape of the Earth, using the price of the cheapest flight available on Kayak.com as a proxy for distance.

February 19 
Caleb Springer 
Abelian varieties from the perspective of modules (Show/hide abstract)


Abelian varieties combine geometry and algebra in one beautiful package. On the one hand, they are smooth projective varieties that can be studied and appreciated purely geometrically. On the other hand, abelian varieties also have an abelian group law on the set of points. In fact, we can view this group as a module in a very natural way. This leads us to ask: Given an abelian variety, can we describe the module structure? We will discuss known results, starting with elliptic curves, in the context of finite fields.

February 12 
(Lunch canceled) 
[PhD defense at this time!]

February 5 
William Noland 
Elliptic Curves and Undecidability (Show/hide abstract)


Elliptic Curves are geometric objects which also carry useful algebraic structure. Hilbert's tenth problem asks if there is an algorithm to determine whether integer polynomials have integer solutions. It turns out that there is a surprising connection between the two. In this introductorylevel talk I will give some basic facts about elliptic curves and their connection to Hilbert's tenth problem in rings of numbertheoretic interest, before outlining a few recent results on the subject (including my own).

January 29 
Ana Chavez Caliz 
Poncelet polygons
(Show/hide abstract)


During his time captive in prison in Saratov, Jean Poncelet developed one of his most important works, Traité des propriétés projectives des figures, establishing the foundations of projective geometry. One of his most famous results is the Poncelet Porism (which gives rise to a special family of polygons known as Poncelet polygons). It is surprising that, even though this result has been around for more than 200 years, we still find questions without an answer relating to these families of polygons.
During this talk, I will present a few recent results and a sketch of the tools and techniques used to solve these problems. The talk will include a glimpse into some open questions in the field.
