# The San Marcos Informal Mathematics In-person Colloquium (SMIMIC)

## Spring 2024

- Thursday, Feb 15: Dr. Brian Katz
**TIME: 12:00-12:50PM****LOCATION: Commons 206**

**Title: How do mathematicians believe?****Abstract:**Love it or hate it, many people believe that mathematics gives humans access to a kind of truth that is more absolute and universal than other disciplines. If this claim is true, we must ask: what makes the origins and processes of mathematics special and how can our messy, biological brains connect to the absolute? If the claim is false, then what becomes of truth in mathematics? In this session, we will discuss beliefs about truth and how they play out in the mathematics classroom, trying to understand a little about identity, authority, and tertiary education.**Speaker Info:**Brian P Katz (BK) is faculty in Mathematics Education and coordinator for the Math Single Subject Credential at CSULB, part of the leadership teams of RUME SIGMAA, the SoCal-NV Section of the MAA, the journal PRIMUS, the inclusion/exclusion blog, and Project NExT. - Thursday, Feb. 22: Dr. Kate Stevenson
**TIME: 12:00-12:50PM****LOCATION: Commons 206**

**Title:****The Power of a Broad View of Mathematics****Abstract:**Recently, the Mathematics Department at CSUN instituted a problem solving class for mathematics majors. The goal is to create an experience that is closer to how mathematicians work across and between fields to expand the frontiers of mathematics. In this talk, we will discuss how geometry, topology, and algebraic geometry inspire and inform one another. We will start by reviewing some basic properties of**R**and**C**that allow us to build covering spaces of curves by working very locally. We will touch on how Riemann and others used such local analysis to understand functions between Riemann Surfaces (which are curves themselves when viewed as complex spaces). Then we’ll see some results from algebraic geometry that used and modified these analytic techniques to better understand curves over other fields and Galois extensions of**Q**. Finally, if time is left, we will close with a glimpse of recent award winning results on Riemann Surfaces and the moduli spaces that parameterize them that were informed by areas as diverse as billiard balls and conic sections. - Thursday, Feb. 29: Dr. Mary Pilgrim
Collaborative Colloquium with CRESE

**TIME: 12:00-12:50PM****LOCATION: UNIV 100****Mary Pilgrim's Website**

- Thursday, March 14: Dr. Laird Kramer
Collaborative Colloquium with CRESE

**TIME: 12:00-12:50PM****LOCATION: UNIV 100****Speaker Profile**

- Thursday, March 28: Dr. Badal Joshi
**TIME: 12:00-12:50PM****LOCATION: Commons 206**

**Title: Chemical mass-action systems as analog computers: implementing arithmetic computations at specified speed****Abstract:**DNA-strand displacement and other technological advances have made it possible to implement computation in a (wet) cellular environment. Reaction networks, and associated mass-action kinetics, can therefore, be treated as a programming language for analog computation. The challenges of using nonlinear differential equations to perform computation are different from the ones that are faced when using Boolean algebra in digital computers. On the positive side, differential equations can be solved without a discrete approximation. On the other hand, implementing discrete processes such as arithmetic and algebra is less straightforward. Previous authors had shown how to implement basic arithmetic operations (addition, subtraction, multiplication, inversion etc.) using a reaction network-based computer, but had not considered the critical element of speed of computation. In our work, we develop ``chemical modules'' that carry out basic arithmetic operations and we prove that the developed modules have a speed of computation that is independent of the inputs. Moreover, we prove that these elementary modules can be run in parallel so as to carry out any desired arithmetic computation, also at speed that is independent of input. - Thursday, April 4: Dr. Amy Buchmann
**TIME: 12:00-12:50PM****LOCATION: Commons 206**

**Title: Modeling Microscale Biofluids****Abstract:**Mixing and pumping at a microscopic level is very challenging due to the counter-intuitive hydrodynamics that occur on this scale. However, bacteria have evolved to swim in this environment, so the helical flagella of bacteria may inspire new designs for man-made devices. Understanding the hydrodynamics of microscale, rigid, rotating helices immersed in a fluid is crucial to inform the creation of new devices. I will show how mathematical modeling can play an important role in this study and highlight some topics in the undergraduate mathematics curriculum that I use in my models. - Thursday, April 11: Advancement to Candidacy, Guillermo Jimenez
**TIME: 12:00-12:50PM****LOCATION: Commons 206**

CSUSM master's student Guillermo Jimenez will be giving his advancement to candidacy talk.

- Tuesday, April 23: Dr. Álvaro Lozano-Robledo gives the Reid Lecture
**TIME: 6:00-8:00 PM****Álvaro Lozano-Robledo's Website**

- Thursday, April 25: Thesis Defense, Iryna Razhkova
**TIME: 12:00-12:50PM****LOCATION: Commons 206**

CSUSM master's student Iryna Razhkova will be defending her thesis.

**Title: Sofya Kovalevskaya and the Cauchy-Kovalevskaya Theorem****Abstract:**Born and raised in Russia in the middle of the 19th century, Sofya Kovalevskaya had no chance to obtain a higher education in Russia because of her gender. Overcoming various barriers, she ended up moving to Europe, but faced new obstacles as a woman in mathematics and science. She wanted to study, be independent and have a career, which was prohibited in many European countries in the 19th century. Moreover, she wanted to study mathematics, which considered a male domain at that time.

Managing all obstacles through her tenacity, self-confidence, and hard work, she became the first woman in modern Europe to gain a doctorate in mathematics (at age 24), the first woman appointed to a full professorship in northern Europe (Stockholm University, Sweden), and the first woman to work for the international scientific journal (Acta Mathematica) as an editor.

She died young (at age 41), but she wrote nine articles in mathematics and physics. One of her doctorate dissertations “Zur Theorie der partiallen Differentialgleichungen” (On the Theory of Partial Differential Equations), which today is known as Cauchy-Kovalevskaya Theorem, won her valuable recognition within the European mathematical community. The Cauchy-Kovalevskaya Theorem gives conditions for the existence of solutions to analytic differential equations and became a fundamental result in the study of the class of these equations. - Thursday, May 2: Dr. Nathan Kaplan
**TIME: 12:00-12:50PM****LOCATION: Commons 206**

**Title: Random Groups in Number Theory and Combinatorics****Abstract:**How are random arithmetic objects distributed? In this talk we will ask lots of questions and discuss several examples. The talk will be accessible to a broad audience without a lot of background in algebra or number theory.Here are some examples of the kinds of questions we will consider. How many sublattices of

**Z**^{n}have index at most X? If we choose such a lattice L at random, what is the probability that**Z**^{n}/L is cyclic? What is the probability that the order of this quotient is odd? Now let R be a random subring of**Z**^{n}. What is the probability that**Z**^{n}/R is cyclic? We will see how these kinds of questions connect to subjects like graph theory, algebraic number theory, and the study of random matrices with integer entries.

## Fall 2023

- Thursday, September 28: Dr. Sixian Jin
**TIME: 12:00-1:00PM****LOCATION: Commons 206**

*The Distribution Builder - An innovative tool for decision making: When to sell an asset?*with Dr. SixianJin, Department of Mathematics at CSUSM.An introduction to the innovative and powerful took, “the distribution builder”, for determining the best time to seen an asset. It was originally developed by Nobel laureate Sharpe and his collaborators.

This is a traditional approach to finding the best-selling time that heavily relies on a well-selected “utility function”, which is challenging to describe and needs a lot of math for investors. The core idea of the distribution builder is to encourage investors to express their preferences with a wealth distribution, such as what they aim to achieve at retirement, with much fewer restrictions than choosing a utility function.

- Thursday, October 12: Dylan Scofield
**TIME: 12:00-1:00PM****LOCATION: Commons 206**

*Fermat's Last Theorem for n=4*with CSUSM undergraduate student, Dylan Scofield, Department of Mathematics. Faculty advisor is Dr. Hanson Smith.We will prove that 𝑥⁴ + 𝑦⁴ = 𝑧⁴ has no non-trivial integer solutions. Along the way, we will discuss the history of the famous problem as well as some of the ideas that lead to its eventual full solution.

- Thursday, November 2: Eva Loeser
**TIME: 12:00-1:00PM****LOCATION: Commons 206**

**Title:***Stochastic Network Models with Applications to Biology, Computer Science, and Operations Research***Abstract:**Stochastic processing networks is a subfield of probability that models situations in which “jobs”, often representing customers, packets of data, or travelers, move through often complex systems in which they receive some sort of “processing”, such as customer support, uploading or downloading, or transportation. I will discuss how tools from this field can be used to model situations such as a store checkout counter, a Wi-Fi network, or a call center. However, the talk will be focused on my application of interest: enzymatic processing. I will show you how tools from probability (specifically stochastic networks) can be used to understand the dynamics of enzymatic processing. - Thursday, November 9: Dr. Emily Cilli-Turner
**TIME: 12:00-1:00PM****LOCATION: Commons 206**

**Title:***Assessing Differently: An Introduction to Standards-Based Grading***Abstract:**Have you ever thought about why we grade or if grades we give measure what we want them to? In this presentation, I will introduce the idea of standards-based grading (SBG) and explain how it can be an opportunity to think deeply about these questions while providing students with more equitable grading practices. I will discuss reasons to use this assessment method, introduce some of the big questions one should ask themselves when implementing SBG as well as give examples of implementations from my own classes and from the SBG literature. - Thursday, November 16: Advancement to Candidacy, Iryna Razhkova
**TIME: 12:00-1:00PM****LOCATION: Commons 206**

CSUSM master's student Iryna Razhkova will be giving her advancement to candidacy talk.

**Title:**Sofya Kovalevskaya and the Cauchy-Kovalevskaya Theorem.**Abstract:**Born and raised in Russia in the middle of the 19th century, Sofya

Kovalevskaya had no chance to obtain a higher education in Russia because of her

gender. Overcoming various barriers, she ended up moving to Europe, but faced

new obstacles as a woman in mathematics and science. She wanted to study, be

independent and have a career, which was prohibited in many European countries

in the 19th century. Moreover, she wanted to study mathematics, which considered

a male domain at that time.

Managing all obstacles through her tenacity, self-confidence, and hard work,

she became the first woman in modern Europe to gain a doctorate in mathematics

(at age 24), the first woman appointed to a full professorship in northern Europe

(Stockholm University, Sweden), and the first woman to work for the international

scientific journal (Acta Mathematica) as an editor.

She died young (at age 41), but she wrote nine articles in mathematics and

physics. One of her doctorate dissertations “Zur Theorie der partiallen

Differentialgleichungen” (On the Theory of Partial Differential Equations), which

today is known as Cauchy-Kovalevskaya Theorem, won her valuable recognition

within the European mathematical community. The Cauchy-Kovalevskaya

Theorem gives conditions for the existence of solutions to analytic differential

equations and became a fundamental result in the study of the class of these

equations. - Thursday, November 30: Dr. Harold Polo
**TIME: 12:00-1:00PM****LOCATION: Commons 206**

**Title:***Goldbach meets Laurent***Abstract:**We prove an analogue of the Goldbach conjecture for Laurent polynomials with positive integer coefficients. This talk is based on a joint work with Sophia Liao.

Individuals with disabilities who would like to attend this event please contact the CSUSM Mathematics Department at mathdept@csusm.edu regarding any special accommodation needs. It is requested that individuals requiring auxiliary aids such as sign language interpreters and alternative format materials notify the event sponsor at least seven working days in advance. Every reasonable effort will be made to provide reasonable accommodations in an effective and timely manner.