Department of Mathematics

# Seminar Series

## Upcoming Seminars

**Date and Time: **Wednesday, November 29, 2023, at 12 PM

**Location: **Zoom (hosted by the Computational Research Leadership Council (CRLC))

**Speaker:** Diane Oyen (Los Alamos National Lab)

**Title:** Can we trust machine learning predictions to answer science questions?

**Recent Seminars**

**Date and Time: **Friday, October 13, 2023, at 12 PM

**Location:** PB 013

**Speaker: **Dr. Jesus Juyumaya (Universidad de Valparaiso, Chile) (visiting Fresno State)

**Title: **The Homflypt Polynomial

**Abstract:** In this talk, I will explain the construction of the Homflypt polynomial by Vaughan
Jones. This knot polynomial invariant, together with the Kauffman polynomial, are
fundamental pieces of modern knot theory. The talk will begin by giving the necessary
concepts of knot theory and some elements of algebra to follow up the talk. Additionally,
I will do explicit calculations of the Homflypt polynomial and I will show a sketch
of the construction of the Kauffman polynomial due to Birman and Wenzl.

**Date and Time: **Friday, September 22, 2023 at 9 AM

**Location:** PB 390

**Speakers:** Katherine Kelm, Ph.D.; Mario Banuelos, Ph.D.; Howie Hua, M.A. (Fresno State)

**Title: ***Group Contracts: an Essential Team-Building Tool (Dr. Kelm); Equitable Grading Practices
and Rethinking Assessments (Dr. Banuelos); We are better together (Mr. Hua)*

**Abstracts:**

*Group Contracts: an Essential Team-Building Tool*: In order for students to work successfully in teams, it is essential to scaffold
team-building basics in the course. In particular, having student teams write their
own contracts encourages them to visualize how they will complete tasks as a group,
to have conversations on their expectations for what constitutes a good team player,
and to get practice writing a clear agreement on these principles. In this brief talk
I will describe the activities and prompts I give in my classes in order to help guide
teams toward effective contracts. I will also show samples of student-written contracts
for both upper- and lower-division courses.

*Equitable Grading Practices and Rethinking Assessments*: This talk will cover some equitable grading practices in assessments and the influence
of bias in grading. Examples will be highlighted and will also include alternative
summative assessments in STEM courses.

*We are better together*: This talk will cover how I implement study guides so students can help each other
at any time.

**Date and Time: **Friday, September 8, 2023 at 9 AM

**Location: **PB 390

**Speaker:** Khang Tran, Ph.D. (Fresno State)

**Title: ***On the zeros of certain Sheffer sequences and their cognate sequences*

**Abstract: **This is a joint work with Gi-Sang Cheon from Sungkyunkwan University and Tamas Forgacs
from Fresno State. We study conditions under which the zeros of a sequence of Sheffer
polynomials lie on a critical line Re(s)=c. Through this study, we find uniform asymptotic
formulas for these polynomials and the limiting probability density function for the
zeros of these polynomials on the critical line. Although the proofs are technical,
the motivations and the statements of the results in this talk are accessible for
students.

**Date and Time:** Friday, October 7, 2022 at 9 AM

**Speaker:** Yaomingxin Lu, Ph.D. (Fresno State)

**Title:** *Use of Technology in Assessing Students’ Mathematical Understanding and Supporting
their Productive Struggles*

**Abstract: **In Math Education, tracking students’ thinking process is always a focus when studying
students’ learning and struggles. However, previous research had mainly focus on students’
final product of their work (homework, tests, writing) instead of their moment-by-moment
problem solving/proving processes. In this talk, I plan to explore students’ thinking
process and struggles using Technology tools such as LiveScribe Pen. LiveScribe Pen
captures both audio and real-time writing using a camera near end of the ballpoint
pen with a special paper. The use of the Livescribe pen to capture students’ proving
processes is relatively novel in mathematics education research (e.g., Lew & Zazkis,
2019; Savic, 2015) and, to my knowledge, has not yet been applied to examine undergraduate
students’ struggles. Future research on processes can also adapt Livescribe to capture
students’ moment-by-moment actions. If time allows, I will also talk about using of
another technology tool to support students’ productive struggles in learning of mathematics.

**Location: **Zoom

**Date and Time:** Friday, September 23, 2022 at 10 AM

**Speaker:** Gabor Molnar-Saska (Fresno State)

**Title: ***What is the role of mathematics in a big bank - An introduction to financial mathematics*

**Abstract:** Pricing derivatives is one of the most difficult and exciting problems in the financial
industry. Although it is not possible to

prepare for every possible future scenario, to determine the fair price under certain
assumptions is a purely mathematical question. In this presentation, I will talk about
the basics of option pricing in the binomial world and show its relationship with
probability theory. At the end of the presentation, I will talk about the extension
of the basic model to the continuous world where elements of stochastic calculus are
used as tools.

**Location:** Zoom

**Date and Time: **Thursday, September 29, 2022 at 1 PM

**Speaker:** Gabor Molnar-Saska (Fresno State)

**Title:** *Research in the Academy versus in the Financial Industry*

**Abstract:** The economic world has been changing continuously and today is always different
from what we have seen before in history. In this changing environment scientific
research is very important not only in academia, but also in the financial industry.
Being a practitioner in finance for more than 16 years and also teaching and supervising
master students at the university, in this presentation I would like to highlight
the main similarities and differences between these two fields.

**Location:** Zoom

**Date and Time:** Friday, March 25, 2022 at 9 AM

**Speaker: ** Carmen Caprau

**Location: **Zoom

**Abstract:** In this presentation, we introduce the concept of colored links and construct a
rational function that is an invariant for colored links. Our construction makes use
of colored planar graphs with vertices of degree four. We prove that the corresponding
link invariant yields certain graphical relations for 4-valent planar graphs; these
graphical relations provide an efficient way for computing the invariant of a given
colored link. We also explain how our construction allows for extending the invariant
to another type of links, called colored singular links. This is joint work with
undergraduate students Audrey Baumheckel and Conor Righetti.

**Date and Time:** Friday, October 22, 2021, at 9 AM

**Speaker:** Marat Markin

**Location:** Zoom

**Title:** *On the Chaoticity of Derivatives*

**Abstract:** We introduce sufficient conditions for linear chaos and thereby show that the *n*th derivative with maximal domain is a chaotic operator in the spaces *C*[*a*, *b*] and *L _{p}*(

*a*,

*b*) (-\infty <

*a*<

*b*< \infty) for each

*n*\in \mathbb{N}.

The new results are to be presented for the first time.

### FALL 2021 Seminars

**Date and Time: **Friday, October 7, 2021, at 9 AM

**Speaker:** Tamás Forgács

**Location:** Zoom

**Title:** *Very triangular number – an exploration*

**Abstract:** Very triangular numbers are an example of a subset of the natural numbers with the
property that (i) they are defined by a polynomial f:N -> N, and that (ii) the sum
of their binary digits also belongs to f(N). In this talk we prove a number of results
concerning very triangular numbers and their distribution among the triangular numbers.
We show that their (natural) density within the set of triangular numbers is zero,
and discuss some open questions regarding the existence and length of arithmetic progressions
of very triangular numbers among the triangular numbers

### SPRING 2021 Seminars

**Date and Time: **Friday, April 16, at 8:50 AM

**Location: Zoom link**

**Speaker: **Marat Markin

**Title:** *On Spectral Mapping Theorems and Asymptotics of Scalar Type Spectral C0-Semigroups*

**Abstract: **We establish spectral inclusion and mapping theorems for scalar type spectral operators
and thereby extend a *weak spectral mapping theorem* and a *generalized Lyapunov stability theorem*, known to hold for the C_{0}-semigroups of normal operators on complex Hilbert spaces, to the more general case
of the C_{0}-semigroups of scalar type spectral operators on complex Banach spaces. For such semigroups,
we also obtain a spectral mapping theorem for point and continuous spectrum and exponential
estimates with the best stability constants. Further, we extend to a Banach space
setting the *Gearhart-Prüss-Greiner characterization* of uniform exponential stability for C_{0}-semigroups on complex Hilbert spaces and acquire as an instant corollary a characterization
of uniform exponential stability for scalar type spectral and eventually norm-continuous
C_{0}-semigroups.

### FALL 2020 Seminars

**Date and Time: **Friday, October 30, at 9 AM

**Location:** Zoom link

**Speaker: **Marat Markin

**Title: ***On Weak Spectral Mapping Theorems, **Spectral Structure and Asymptotics **of C _{0}-Semigroups *

*Generated by Scalar Type Spectral Operators*

**Abstract: **We establish a *weak spectral mapping theorem* for scalar type spectral operators and apply it to extend a *weak spectral mapping theorem *and the *generalized Lyapunov stability theorem*, known to hold for the C_{0}-semigroups of normal operators on complex Hilbert spaces, to the more general case
of C_{0}-semigroups of scalar type spectral operators on complex Banach spaces. For such semigroups, we also reveal finer spectral structure, obtain
exponential estimates, and establish an analogue of the *Gearhart-Prüss-Greiner characterization* of the uniform exponential stability for C_{0}-semigroups on complex Hilbert spaces.

**Date and Time: **Friday, October 23, at 9 AM

**Location:** **Zoom**

**Title**: *Automorphism Groups of Spatial Graphs and Hyperplane Arrangements over Finite Fields*

**Speaker**: Oscar Vega

**Date and Time: **Friday, September 25, at 9 AM

**Location:** **Zoom**

**Title**: *Zero distribution of a Sheffer sequence*

**Speaker**: Khang Tran

**Abstract**:

**Date and Time: **Friday, September 11, at 9 AM

**Location:** Zoom

**Title**: *Studying Heuristics and Problem Solving: **Highlights of my work during **My Difference in Pay Leave*

**Speaker**: Agnes Tuska

**Abstract: **As I planned in my Difference in Pay Leave application for the 2019-2020 academic
year, I helped Dr. Andrew Benedek to organize and run the 2nd International Conference
on Heuristics: Motivating, Orienting and Modeling Invention in Balatonfured, Hungary,
August 30-September 1, 2019. The program of the conference is available at the website

https://heurisztika.btk.mta.hu/en/program

As a continuation of our work, I proposed and led the organization of a special session on How to Solve It? Heuristics and Inquiry Based Learning with co-organizers Mario Banuelos and Andrew Benedek for the American Mathematical Society’s Spring Western Sectional Meeting,

California State University, Fresno, May 2-3, 2020

(see https://www.ams.org//meetings/sectional/2272_program_ss18.html#title).

I was a scheduled presenter there. The conference was cancelled due to the pandemic. However, I decided to give the presentation I planned for the AMS meeting on George Polya’s influence on mathematics competitions in the USA at the History of Mathematics & Teaching of

Mathematics International Conference (see https://www.uni-miskolc.hu/hmtm/ ), in which I was a member of the Organizing and Scientific Committee. During April, we re-organized the conference into a virtual conference, still hosted by the University of Miskolc, May 20-24, 2020. Later, as invited speaker, I also presented an extended version of this talk at the online Summer University/Intensive Course on “Central European Contributions to the History of Mathematics and Teaching Mathematics”, organized by the CEEPUS Network, coordinated by the University of Miskolc, July 6-17, 2020. Now I want to share some of my findings with you in the Fresno State community, too!

** **

**If you need a disability-related accommodation or wheelchair access information, please
contact the mathematics department at 559.278.2992 or e-mail ** mathsa@csufresno.edu. **Requests should be made at least one week in advance of the event.**