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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:

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:

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 Requests should be made at least one week in advance of the event.

Archived Seminars