This GEMS session will be facilitated by Professor Qidi Peng and William Wu from Claremont Graduate University. Title: How to create a die if you only have a coin? Abstract: Imagine you have no dice but only coins, how do you play a monopoly game? This lesson introduces a number of mysterious methods to simulate all probabilities […]
Given a polynomial defined over a field $K$, you can build an extension of $K_\infty / K$ by adjoining inverse images of some point $\alpha \in K$. The behavior of these extensions (including the degree , ramification, and associated Galois representations) are surprisingly different in the cases that $K$ is a number field versus a […]
This poster session is meant to showcase undergraduate and graduate work in the mathematical sciences, broadly interpreted, in a supportive environment. The poster session will take place at Claremont Graduate University at The Drucker Institute, 1021 N Dartmouth Ave from 4:15pm - 5:30pm, on Wednesday September 9th, 2026. Refreshments will be provided! For any […]
We showcase Newman's proof of the Prime Number Theorem, published by Don Zagier. Link: https://www.jstor.org/stable/2975232 For questions about the event, please contact your NTLS Organizers: Maxwell Kooiker (Maxwell.Kooiker@cgu.edu) or Prof. Edray Goins (Edray.Goins@pomona.edu)
In multi-armed trials, adaptive designs are a popular way to increase estimation efficiency or identify optimal treatments. Many recent papers have proposed adaptive methods for minimizing the error of unbiased estimators that consider each treatment arm in isolation. This approach may be inefficient, because it fails to borrow shared information across the treatment arms. We […]
Kloosterman sums are explicit exponential sums which occur in several contexts in number theory and arithmetic geometry. Bessel functions encode a great deal of representation-theoretic information about finite groups of Lie type, but they are difficult to compute in general. In this talk, we will carefully define these objects and describe a direct relationship between […]
Abstract: Edge ideals of graphs provide a fertile ground for uncovering combinatorial expressions for algebraic invariants of squarefree monomial ideals. Many algebraic invariants of these edge ideals directly reflect combinatorial properties of their underlying graphs. In this talk, I will discuss how the independence polynomial P_G(x), the generating function for independent sets of a graph G, […]
We showcase Diophantine Representation of the Set of Prime Numbers by Jones, Sato, Wada and Wiens. Link: https://www.jstor.org/stable/2318339 For questions about the event, please contact your NTLS Organizers: Maxwell Kooiker (Maxwell.Kooiker@cgu.edu) or Prof. Edray Goins (Edray.Goins@pomona.edu)
A Belyĭ pair \bigl( S,\, z(w) \bigr) is a compact, connected Riemann surface S together with a rational function z \colon S \to \mathbb{P}^1(\mathbb{C}) which has at most three critical values \bigl\{ 0,\, 1,\, \infty \bigr\}. The preimage z^{-1}\bigl( \bigr) \subseteq S \hookrightarrow \mathbb{R}^3 is a bipartite graph called a Dessin d'Enfant. When S = \mathbb{P}^1(\mathbb{C}) […]
The unique minimal generating set for a semigroup of lattice points in an n-dimensional polyhedral cone is called its Hilbert basis. In the case when the cone is spanned by lattice points, this Hilbert basis is finite, however its cardinality can be much larger than n. Nevertheless, a conjecture of Sebö states that each point […]
Speaker: Sam Nelson (CMC) Title: Permutation Jones Polynomials Abstract: The Jones Polynomial is an important invariant of knots with applications in physics, quantum computation and more. In this talk I will introduce a family of generalizations of the Jones polynomial associated to permutations of finite sets and discuss their properties. _______ We especially welcome all […]
Flyer for Kim's talk. Abstract: The logistic map is one of the most famous examples in dynamical systems. Originally introduced as a simple model of population growth, it exhibits a surprisingly rich range of behavior: as a single parameter varies, stable equilibria give way to periodic orbits and eventually to chaos. But in real populations, […]
