Archive of Some Previous Speakers and Talks
Talks (Fall 2021- Spring 2022 )
Date: 4:00 pm on
Monday, August 30, 2021(AC1-101)
Speaker:
David Jekel,
UCSD
Title: TBA
Abstract:
We *strongly encourage* mask-wearing for the safety of all of us.
Talks (Fall 2017- Spring 2018 )
Date: 4:00 pm on Thursday, September 14, 2017 (AC-247)
Speaker: Tomasz Odrzygozdzi,
Institute of Mathematics PAN, Poland
Title: Exotic Property (T)
Abstract: I will introduce the concept of Kazhdan’s Property (T), which is one of the main concerns of modern Geometric Group Theory. This is a property which on one hand has a number of applications but on the other it’s very hard to provide examples of (apart from some trivial cases). I will try to explain why Kazhdan’s Property is so exotic and important.
Date: 4:00 pm on Tuesday,
October 24, 2017 (AC-247)
Speaker: Sam Spiro,
UCSD
Title:
Polynomial Relations of Matrices of Graphs
Date: 3:00
pm on Friday, November 10, 2017 (AC-247)
Speaker:
Chi-Kwong Li ,
College of William and Mary, Virginia
Title:
Numerical Ranges and Dilations
----Second Biannual Paxxon Conference on Algebra and Discrete Mathematics---
Abstract: Growth
in groups was introduced by Milnor in 1968.The growth of a group is closely
related to the growth of its associated group algebra over a field of
characteristic zero. We recall some major historical results on growth in
groups, then focus on Gromov's concept of uniform exponential growth. We
strengthen a result of Alperin by proving the group algebra of a free abelian by
infinite cyclic group over a field of characteristic zero is of polynomially
bounded or uniform exponential growth.
Date: 4:15 pm on Thursday
June 8, 2017 (AC-115)
Speaker:
Kazu Nishinaka
Title: TBA
----The Fifth Annual Conference for the Exchange of Mathematical Ideas ----
Abstract: I
will explain the discrete log problem and why it’s relevant to cryptography. I
will then go on to introduce digital signal processing to the study of elliptic
curves over finite fields. After that I will show how digital smoothing
operators can be used to attack the discrete log problem in a new way.
Abstract: The growth of groups and their group algebras are closely connected; results on the group algebra strengthen results on the group. We discuss some results in pursuit of an analog to the 2008 result of Breuillard and Gelander on the uniform exponential growth of linear groups. We discuss a theorem on the growth of a semidirect product of a linear group by an infinite cyclic group, and use this to demonstrate uniform exponential growth of some poly-Z algebras. We offer conjectures on a path forward and discuss challenges in considering algebra growth versus group growth.
Date: 4:10 pm on Friday, October 16, 2015 (AC-247)
Abstract: We use the discharging method to prove that every 3-connected, essentially 10-connected line graph is hamiltonian connected.
Date: 4:10 pm on Friday, November 6, 2015 (AC-247)
Abstract:
The numerical range of a bounded operator T acting on a complex
Hilbert space H is the collection of numbers (Tx, x), where ( , ) denotes the inner product on H and x
ranges over the unit vectors of H.
The numerical radius of T is the supremum of the moduli of
elements of the numerical range of T, and defines a norm on B(H).
There are many generalizations of numerical range and numerical radius;
most such generalizations have associated semi-norms, if not norms.
We investigate the problem of when is a linear map an isometry for a certain generalized numerical radii.
Abstract: The card game set has entertained mathematicians and laypeople alike for decades. Much literature on the game concerns the probability of a set existing in a given hand; little has been written about mathematically-informed strategic play. In this talk we introduce the game and discuss some historical results, then develop and prove the worth of a strategy of play. We explore the properties of some algebraic objects which naturally arise from the investigation.
Abstract: The study of cellular automata has a long history in mathematics, dating back to the work of von Neumann. The classical example of a cellular automaton is Conway's Game of Life, which is played on the integer lattice \mathbb{Z}^2, where which each point is considered to have one of two states: alive or dead. After one unit of time has elapsed, a cell’s new state is determined by its current state and the current state of its neighbors. Viewed globally, the Game of Life takes the form of a mapping \tau : \mathcal{C} \rightarrow \mathcal{C}, where \mathcal{C} is the space of all possible configurations of living and dead cells on \mathbb{Z}^2.
Early questions about the Game of Life concerned the existence of
patterns which exist only in a cellular automaton’s initial configuration. Such
patterns are fittingly called Garden of Eden patterns. In the 1960s, Moore and
Myhill proved that the Game of Life admits Garden of Eden patterns if and only
if it admits mutually erasable patterns. More recent results extend this
characterization to cellular automata supported on spaces much more general than
\mathbb{Z}^2. In particular, we will discuss an result of Ceccherini-Silberstein,
Machi, and Scarabotti that proves a Moore-Myhill-type characterization for
cellular automata played on finitely generated amenable groups.