Greenslopes Seminar FA14 [Department of Mathematics] Thursdays 11 AM Weber 223 Co-Organizers: Josh Maglione and Rachel Neville

Schedule:

For the seminar attendance sheet, click here.
Abstracts appear below.

Abstracts:

Sept 4 -The Spectrum of an Equivariant Cohomology Ring by Quillen - Mark Blumstein
In this talk I will nonchalantly toss around a bunch of algebraic topology jargon until some interesting results by Quillen appear on the board, literally by magic*.

In the process I hope to relate some basic constructs and ideas in algebraic topology to those who have no experience in the area, while still getting to Quillen's more interesting results.Specifically I will discuss the construction of universal bundles (with easy examples!), equivariant cohomology, and sketch a proof of the finiteness theorem (i.e. given the right conditions, an equivariant cohomology ring is finitely generated). With the finiteness theorem, tools from algebraic geometry may be thrown in the mix and I will state the main result of the first paper of this series, which gives a formula for calculating the dimension of an equivariant cohomology ring. Time permitting, I will state a result or two from the second paper.

* By literally, I meant not at all literally, you were supposed to figure that out from the context of the paragraph. Thus concludes my first lesson on how to read anything an algebraic topologists writes.

Sept 11 - Cohomology is a word that is used a lot in math.... - Douglas Ortego
I am aiming this talk at students who are sick and tired of the buzzword 'cohomology.' If the phrase "it's a simple cohomological argument" is annoying to you, maybe I can help a little. The definition of a cohomology ring and several ways of thinking about it along with examples will take up the time of the talk. It will also (hopefully) make listening to other student's or researcher's talks involving this damned ring more palatable. If there is time, I'll show some neat combinatorics that gives you efficient ways of computing things in cohomology rings of particularly common spaces [Grassmannians].

Sept 18 - Counting Points and Why You Should Love \mathbb{F}_p - Ryan Becker
In this talk, we will give some motivation for why one might care about finite fields (Douglas' disparaging comments notwithstanding) and curves defined over them. We will walk through several novel examples of counting points on curves and on varieties more generally. To conclude, we will derive the well-known Hasse-Weil bound in the ordinary way as well as by appealing to a cohomological dimensionality argument.

Sept 25 - Counting Curves, Stable Maps, and Gromov-Witten Invariants - Vance Blankers
Enumerative geometry--counting geometric objects that satisfy certain specified conditions--is a topic that occupied some of the earliest mathematicians. In this talk we aim to define (genus-zero) Gromov-Witten invariants and to provide an idea as to why these objects are relevant to answering certain geometric counting problems. Along the way, we'll discuss moduli spaces and (time-permitting) the "right" way to think about integrals.

Oct 2 -Nematic liquid crystals and cell membranes- Mike Mikucki
In this talk, I will derive the mechanical energy for pure lipid membranes. In my research, I have used the formulation of this energy many times, simply trusting in the results of two papers published in 1958 and 1973. Ironically, toward the end of my PhD career, I finally made my way through the details of these foundational papers. In this presentation, I will first discuss the advantages and disadvantages of this seemingly backwards approach to research. Then, I will present the mathematical derivation of the energy from the papers. Finally, I will mention some shortcomings of the model based on the assumptions made in the papers.

Oct 9 -A Kinetic Model for HIV-1 Viral Capsid Nucleation- Farrah Sadre-Marandi
The viral capsid acts as a protective shell for the genetic material (DNA or RNA) of virus. Viral capsid assembly goes through the nucleation and elongation stages. After maturation, a virus is able to attack new host cells and replicate its DNA or RNA, leading to virus spread throughout the host body. Therefore, it is of great interest to characterize favorable, restrictive, and prohibitive conditions for viral capsid assembly so that antiviral therapies can be developed. This talk presents a mathematical model developed specifically for the nucleation of HIV-1 capsid. Numerical simulations of HIV-1 capsid nucleation are conducted using a 6-species dynamical system model. Deterministic and stochastic factors in this process will be examined as well as the sensitivity of the system behavior to model parameters. This research was funded by an NSF EAPSI award during the speaker’s visit to Wuhan University in China and with the collaboration of the Chinese Ministry of Science and Technology.

Oct 16 -The Orb Family-Anne Ho
Once upon a time, there lived a family of orbs with four children. Of these children, the oldest three were identical triplets. Being a mischievous trio, they liked to confuse neighbors, schoolteachers, and strangers alike as to who was who. In my talk, I will relate the story of the Orb family and how they are tied to my research.

Oct 23 -- Patrick O'Leary
Dr. O'Leary is a research scientist at Kitware, which is a leader in the creation and support of open-source software and state of the art technology. He will discuss life after grad school and what it’s like working for Kitware.

Oct 30 -Inverse Problems and EIT- Micheal Capps
In this talk I will give an introduction to inverse problems and introduce the electrical impedance tomography (EIT) problem. I will also discuss my work in the separation of ventilation and cardiac signals in a sequence of chest images made using EIT and how this could be used to monitor pulmonary perfusion in a patient (and why current methods aren't ideal).

Nov 6 -Numerical Algebraic Geometry- Tim Hodges
Given a system of n polynomials and m variables is it possible to solve for when this system is zero? The aim of this talk is to give an introduction to how the software Bertini solves a polynomial system. As well as, talk about two interesting aspects of numerical algebraic geometry namely, ramification points and syzygies.

Nov 13 -Combinatorial Nullstellensatz - Ben Cooper
We state and prove a result of N. Alon - "Combinatorial Nullstellensatz", and discuss a few applications. In particular, we use it to (easily) prove a classical result conjectured by Artin in 1934 and proved by Chevalley and Warning in 1935.

Nov 20 -A Machine Learning Approach to Inverse Problems with Poor Data- Chad Waddington
This talk comes from work begun this summer in Vancouver and which I have continued until recently. The problem involves data taken from accelerometers on a seismic imaging truck and focuses on an attempt to differentiate good and bad imaging data without the ability to actually look at the imaging data itself. I will talk about how many standard approaches failed and how I ultimately succeeded with a machine learning approach. The talk will assume no knowledge of the basic mathematics and should be easily accessible to everyone.

Dec 4 -p-groups, algebras, and bilinear maps- Josh Maglione
We'll start by discussing p-groups and why they can be rather difficult to distinguish. Using methods of Philip Hall and Michel Lazard, we'll move into the realm of Lie algebras. With this connection we're able to `linearize' our group and appeal to the methods of linear algebra. Recent work by James Wilson shows that we can gather a significant amount of new information about the p-groups we started with from bilinear maps associated to these Lie algebras. I'll conclude with a theorem that makes this a bit more precise.

Dec 11 -Snowflake Modelling - Rachel Neville
I will give a brief talk on the some of the math that goes into simulating digital snowflakes after which we will model our own snowflakes with paper using precise methods of folding, cutting, and if you must, gluing.

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