Department of Mathematics

# GAUSS (Graduate and Undergraduate Students Seminar)

## Upcoming Seminars

**When:** Friday, September 23, 2022, at 3:00pm in PB 13

**Presenter:** Anthony Cortez (Fresno State double major Math and Physics)

**Title:** Self-Organized Sacrifices: Ecological Resilience in Worsening Conditions

**Abstract: **In ecosystems that cannot sustain dense uniform vegetation, patterns of concentrated
vegetation emerge to leverage the benefits of dense growth and economize overall resources.
As environmental conditions change, such patterns adapt by varying the spacing between
and the number of vegetated regions. In a prototypical model for pattern formation,
the complex Ginzburg-Landau equation, we study the dynamics of patterned solutions.
As parameters in the equation shift, solutions with dense patterns become less favorable,
and the system transitions to a more sparsely distributed pattern. We propose a method
to predict the timing and overall effect of transitions caused by parameter changes.

## Past Seminars

**When: **Friday, April 29, 2022, at 4:00pm Hybrid (in person in PB 13 and on Zoom: https://fresnostate.zoom.us/j/96299826297)

**Presenter:** Anthony Cortez (Fresno State double major Math and Physics)

**Title:** On Dense Orbits of the Tent Map

**Summary of the talk:** The audience will briefly be introduced to some of the theory of discrete dynamical
systems. This theory will then be used to analyze the tent map, a basic example of
a dynamical system that exhibits behavior referred to as chaos. Along with showing
the tent map is chaotic, we provide proof that no rational number will have a dense
orbit under the tent map.

**When:** Friday, April 22, 2022, at 4:00pm Hybrid (in person in PB 13 and on Zoom: https://fresnostate.zoom.us/j/96299826297)

**Presenter: **Dairah Heinz (Fresno State student)

**Title: **Numerical Methods for Determining Eigenvalues of Matrices in Python

**When: **Friday, April 23, 2021, at 5:00pm via Zoom

**Presenters:** Anthony Cortez and Dhan Bautista (Fresno State students)

**Title:** An Introduction to Quantum Computation via the Deutsch-Jozsa Algorithm

**Abstract:** Quantum computation is a rapidly developing field utilizing features of quantum physics
to develop new computational algorithms. Superposition is a key feature of quantum
mechanics utilized in quantum computation where a quantum particle can be in multiple
states at once. This means that quantum bits or `qubits' can encode more information
than classical bits which are confined to being exactly 0 or 1 whereas qubits may
be expressed as a combination 0 and 1. The scope of its capabilities are still being
discovered, but important cases exist where quantum computation demonstrates a significant
advantage over classical computing. This paper first develops the essentials for studying
quantum computation and applying that knowledge to analyze the Quantum Deutsch-Jozsa
algorithm, which is regarded as the first quantum algorithm formulated that demonstrated
the vast potential advantage of quantum computing.

**When:** Friday, April 23, 2021, at 5:30pm via Zoom

**Presenter:** Vathana To (Fresno State student)

**Title:** On Creating R Packages with an Application in Describing and Simulating Zero-Inflated
Data

**Abstract:** Demand for skills in statistical programming has been rising, and so has found its
way in the standard curriculum of many undergraduate STEM programs. In this talk,
we present the process of creating statistical software packages, units of reproducible
and shareable code, in the R programming language. We cover three core components
in the package creation process: code organization, documentation and testing, and
version control. We also expand on the steps to publish packages for public use through
the Comprehensive R Archive Network (CRAN). We apply these concepts by demonstrating
and elaborating on the process to create ZimulatE, an R package for describing and
simulating zero-inflated data.

**When:** Friday, December 4, 2020, at 4:30 pm via Zoom

**Presenter:** Travis Walker (Fresno State student)

**Title:** Quarantine and its Effects on a Pandemic

**Abstract:** This paper is exploring the different aspects of the COVID-19 pandemic that is affecting
the world. Different techniques or methods in quarantining individuals upon detection
of the virus will be explored. If quarantine is enacted more quickly and to a more
extreme degree, such as a dedicated quarantine zone with no chance of interaction,
will this lead to fewer cases over time, and would this be significantly effective?
Would it be worth considering when compared to the current self quarantining strategy
enacted? The results from this model may be significant in providing a different perspective
on quarantine practices or providing a basis to expand upon the ideas presented in
this paper.

**When:** Friday, December 4, 2020, at 5:00 pm via Zoom

**Presenter:** Jose Mireles (Fresno State student)

**Title:** Modeling the Covid-19 Pandemic

**Abstract:** The models and findings discussed in this paper focus more on the threat caused by
epidemics and their differing effects on different societies and, specifically, those
caused by novel strains such as the COVID-19 pandemic. The proposed solutions to this
problem make assumptions based on information and models on other viral diseases such
as the influenza virus. Specifically, our paper will explore the different effects
of the COVID-19 virus on rural, suburban, and urban areas and how the development
of a vaccine will affect the overall spread of the virus. We will also be exploring
how this information can be used to model the current ongoing COVID-19 pandemic. Combining
our results with those of the previous studies will provide us with insight on how
to fight and prepare for future epidemics.

**When:** Friday, April 26, 2019, at 4:00 pm in PB 012

**Presenter:** Jack Luong (Fresno State student)

**Title:** Properties of Explicit Solutions to the Radial Total Variation Flow

**Abstract:** Suppose all but part of an image is corrupted, and the non-corrupted part is enclosed
in some boundary. By using the non-corrupted information within the boundary, we
can denoise the rest of the image. This process is described by the partial differential
equation called the* Total Variation Flow (TVF). *By considering the radial formulation of the TVF, we find explicit solutions given
a specific type of initial data, and show how we can use these explicit solutions
to approximate a more general class of initial data. We will also introduce some
necessary concepts such as convergence, compact sets, and L^1 spaces - so no serious
math background is required!

**When:** Friday, March 1, 2019, 5:00-5:30 pm in PB 012

**Presenter:** Summer Al-Hamdani (Fresno State student)

**Title:** Applications of Group Theory in Molecular Spectroscopy

**Abstract:** Spectroscopy is the study of the interaction between matter and electromagnetic radiation.
Through spectroscopy, we can study the composition and structure of matter at the
molecular level, the macroscopic level, and even over astronomical distances. Many
of the rules dictating spectroscopy and the complex problems that arise follow from
the symmetry of the problem. Consequently, we can define groups to better describe
the symmetry of a molecule and relate that symmetry to its physical properties. We
will discuss the conceptual basis for groups that describe various physical properties
of molecules.

**When:** Friday, February 1, 2019 at 4:00 pm in PB 012

**Presenter:** Dr. Przemyslaw Kajetanowicz (Fresno State)

**Title:** The Flavor of Exploring Mathematics with your Computer

**Abstract:** How about seeing math come alive in front of your eyes? Watching math concepts in
action? We will take a trip into selected topics in mathematics with the assistance
of GeoGebra - a piece of powerful yet easy-to-use software with amazing capabilities.
From elementary mathematics to multivariate calculus to differential equations to
linear algebra, we will be experiencing the flavor of interweaving math rigor with
computer-aided experimentation. A brief introduction to GeoGebra functionality will
also be given, to enable you to start experimenting on your own.

**When:** Friday, December 7, 2018 from 4:00-4:30 pm in PB 012

**Presenter:** Miguel Bueno (Fresno State student)

**Title:** The Effectiveness of Regulatory Policies in Reducing Airbnb's Presence in Local Markets

**Abstract:** The growth of the sharing economy has received increasing attention from economists
and policy-makers. Airbnb, an online home-sharing platform based out of San Francisco,
has remained at the forefront of the discussion. Recent literature suggests that by
restricting the supply of housing, Airbnb exacerbates the current affordability crises
plaguing many US cities (Horne and Merante 2017, 19-24), potentially gentrifying neighborhoods
and displacing residents (Lee, 2016, 243). Such concerns have prompted policy-makers
to regulate the home-sharing platform by implementing occupancy taxes (Erb 2017),
executing “Cool Dow Periods”, issuing short-term-rental permits (San Francisco
Office of Short Term Rentals,n.d.), and/or limiting the number of days listings are
available (Booth 2016). While recent policy decisions have drawn criticism from critics
and advocates of Airbnb alike, the effectiveness of such policy implementations has
not been measured. This research aims to empirically estimate the effectiveness of
such policies. In particular, the removal of thousands of Airbnb units who failed
to register with the City of San Francisco by January 2018. If there is a notable
effect on residential rental prices, economic theory dictates this could be attributed
to a decline in the supply of Airbnb units – ceteris paribus.

**When:** Friday, December 7, 2018 from 4:30-5:00 pm in PB 012

**Presenter:** Chris Newmark (Fresno State student)

**Title:** The Statistics of Bitcoin

Abstract: Bitcoin has become very popular over the last several years. Among the 2099 different crypto-currencies, Bitcoin is the most popular - and continues to be a source of inspiration and controversy. Investment institutions are taking a serious interest in Bitcoin, but just how risky is this new digital currency? In this talk, we explore some basic statistical topics applied to Bitcoin. We will then give an overview of Extreme Value Analysis and show how this branch of statistics can be used to determine the risk associated with Bitcoin.

**When:** Friday, October 12, 2018 at 4 pm in PB 012

**Presenter:** Oscar Castanos (Fresno State student)

**Title:** On Volterra Quadratic Stochastic Operators of a Two-Sex Population

**Abstract:** We consider a family of operators which model the behavior of a current generation
and its trajectory for future generations. We observe the fixed points of our operators
and the way trajectories behave around these fixed points. We use the eigenvalues
of the Jacobian matrix of our operator to find the type of fixed points of the operator.

**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.**