## Calendar of Events

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### The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong, UC Irvine)

### The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong, UC Irvine)

Given a prime p, let P(t) be a non-constant monic polynomial in t over the ring of p-adic integers. Let X(n) be an n x n uniformly random (0,1)-matrix over the same ring. We compute the asymptotic distribution of the cokernel of P(X(n)) as n goes to infinity. When P(t) is square-free modulo p, this […]

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### Reading Topology from Open Books (Prof. Bahar Acu, Pitzer College)

### Reading Topology from Open Books (Prof. Bahar Acu, Pitzer College)

Title: Reading Topology from Open Books Speaker: Bahar Acu, Department of Mathematics, Pitzer College Abstract: How can we study topological shapes that are outside the realm of our imagination? In this talk, we will explore potential answers to that question by diving deep into dimensionality and topology via open books. Topology is the study of properties of shapes that […]

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### Applied Math Seminar: Ivy Xiong (USC)

### Applied Math Seminar: Ivy Xiong (USC)

Title: A common pathway to cancer: oncogenic mutations abolish p53 oscillations. Abstract: The tumor suppressor p53 oscillates in response to DNA double-strand breaks, a behavior that has been suggested to be essential to its anti-cancer function. Nearly all human cancers have genetic alterations in the p53 pathway; a number of these alterations have been shown to […]

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### Noise stability of ranked choice voting (Steven Heilman, USC)

### Noise stability of ranked choice voting (Steven Heilman, USC)

Given votes for candidates, what is the best way to determine the winner of the election, if some of the votes have been corrupted or miscounted? As we saw in Florida in 2000, where a difference of 537 votes determined the president of the United States, the electoral college system does not seem to be […]

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### Wallis and Landen: A Tale of two integrals (Prof. Victor Moll, Tulane University)

### Wallis and Landen: A Tale of two integrals (Prof. Victor Moll, Tulane University)

Title: Wallis and Landen: A Tale of two integrals Speaker: Victor Moll, Department of Mathematics, Tulane University Abstract: Victor Moll Abstract I was born in Santiago, Chile during the last millenium, on October 31st. My father was a doctor in a small town. I must have been bothering my family, so they put me […]

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### Radial solutions to semilinear elliptic partial differential equations (Professor Alfonso Castro, HMC)

### Radial solutions to semilinear elliptic partial differential equations (Professor Alfonso Castro, HMC)

Using elementary methods from differential equations and analysis we will consider the existence and multiplicity of solutions to semilinear partial differential equations with boundary conditions.

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### Discrete Calculus through generating functions (Wai Yan Pong, Cal State Dominguez Hills)

### Discrete Calculus through generating functions (Wai Yan Pong, Cal State Dominguez Hills)

Discrete Calculus studies discrete structures, such as sequences and graphs, using techniques similar to those used in Calculus for continuous functions. The basic idea of generating functions is to associate a function with a sequence so that the coefficients of the power series expansion of the function represent the terms of the sequence. They provide […]

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### Sequential: A Meditation on Recurrence (Prof. Ghassan Sarkis, Pomona College)

### Sequential: A Meditation on Recurrence (Prof. Ghassan Sarkis, Pomona College)

Title: Sequential: A Meditation on Recurrence Speaker: Ghassan Sarkis, Department of Mathematics, Pomona College Abstract: Though I will share some adventures in sequence-generating neural networks just for fun, the majority of this talk will be concerned with Fibonacci sequences modulo $p$ and $p^2$ from data-inflected and number-theoretic perspectives, including questions about periods of the modular […]

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### Systems of homogeneous polynomials over finite fields with maximum number of common zeros (Sudhir Ghorpade, IIT Bombay)

### Systems of homogeneous polynomials over finite fields with maximum number of common zeros (Sudhir Ghorpade, IIT Bombay)

It is elementary and well known that a nonzero polynomial in one variable of degree d with coefficients in a field F has at most d zeros in F. It is meaningful to ask similar questions for systems of several polynomials in several variables of a fixed degree, provided the base field F is finite. […]

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### A Brief History of Calculating Machines (Prof. Yousef Daneshbod, University of La Verne)

### A Brief History of Calculating Machines (Prof. Yousef Daneshbod, University of La Verne)

Title: A Brief History of Calculating Machines Speaker: Yousef Daneshbod, Department of Mathematics, University of La Verne Abstract: Calculating machines are digital or analog devices designed to perform mathematical calculations. These machines have a long history, with the earliest known examples dating back to ancient times, when people used sticks and stones for counting. However, the […]

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### Bias in cubic Gauss sums: Patterson’s conjecture (Alex Dunn, CalTech)

### Bias in cubic Gauss sums: Patterson’s conjecture (Alex Dunn, CalTech)

We prove, in this joint work with Maksym Radziwill, a 1978 conjecture of S. Patterson (conditional on the Generalized Riemann Hypothesis) concerning the bias of cubic Gauss sums. This explains a well-known numerical bias in the distribution of cubic Gauss sums first observed by Kummer in 1846. One important byproduct of our proof is that […]

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### Career Pathways in the Mathematical Sciences (ONLINE)

### Career Pathways in the Mathematical Sciences (ONLINE)

In this panel we will have people from diverse backgrounds talking about their career pathways. The event will be fully online in the following link: https://cgu.zoom.us/j/89142368885?pwd=YkhkV24zbUZRV0p2d2xEelZtUmFmdz09Meeting ID: 891 4236 8885Passcode: 314159 We will have panelist's introductions at the beginning, and then the remaining time in breakout rooms so that our students and faculty can ask more […]