Department of Mathematics

# Seminar Series

## Upcoming Seminars

TBA

**Recent Seminars**

**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

**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

**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

**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!

**FALL 2019**

**Date and Time: **Friday, November 8, 2019, at 9 AM

**Location:** PB 032

**Title**: *On the Gevrey Ultradifferentiability of Weak Solutions of an Abstract Evolution Equation*

**Speaker**: Marat Markin

**Abstract: **

**Date and Time: **Friday, October 18, 2019, at 9 AM

**Location:** PB 032

**Title: ***Two-intersection sets in the project space PG(3,9)*

**Speaker: **Morgan Rodgers

**Abstract: **

**Date and Time: **Friday, September 27, 2019, at 9 AM

**Location:** PB 032

**Title: ***Rainbow Spanning Trees in Edge-Colored Complete Graphs*

**Speaker: **Katherine Perry, Ph.D. (Soka University)

**Abstract: **

** **

**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.**