Department of Mathematics
GAUSS (Graduate and Undergraduate Students Seminar)
Upcoming Seminars
We shall return in Fall 2024. Have a great summer!
Past Seminars
When: Friday, April 12, 2024 at 3:00pm in PB 013
Presenter: Ricardo Suarez (Ph.D. Candidate, CSU Channel Islands)
Title: Understanding Clifford Algebras and Exterior Algebras
Abstract: We will use the vector space and attach the notion of a null quadratic form in it, this will generate a Clifford algebra isomorphic to the exterior algebra as vector spaces. We then will go on to define Clifford multiplication as well as some elementary properties. This talk should be accessible to anyone with Linear algebra background!
Short Bio: Ricardo is currently a lecturer at CSUCI. He will receive his doctorate in mathematics from UNITO ( University of Torino Italy), for his studies on spinor Abelian varieties. Ricardo’s research interests include Abelian varieties, Clifford algebras ,spin geometry, as well as spin manifolds in differential geometry. He was born in Santiago, Chile, and likes to travel to do mathematics (has been to many countries like Poland, England, Spain and Italy).
When: Friday, October 13, 2023 at 2:00pm in PB 013
Presenter: Dr. Oscar Vega (Fresno State faculty)
Title: Is there anything special about the number 17? Yes, come to the talk
When: Friday, September 22, 2023 at 2:00pm in PB 013
Presenter: Nipun Amarasinghe
Title: Tangles, Webs and an sl(3) invariant
Abstract: Come learn about Nipun's research in knot theory and some of its connections with category theory - an area in mathematics that helps with describing various mathematical structures. There will be lots of pictures.
When: Tuesday, May 2, 2023 at 1:00pm by Zoom
Presenter: Gabriel R. Villarmea
Title: Analysis of Heart Disease using Machine Learning
Abstract: Heart disease is a leading cause of mortality globally. Early detection and intervention are key in mitigating the disease's impact on patients. Machine learning techniques have been used to predict heart disease presence, aiding in earlier diagnosis and better patient outcomes. Logistic regression is a popular technique for binary classification, making it ideal for heart disease prediction. This study will involve using Microsoft Excel as well as R Studio, a math programming language for statistical computing and graphics, to analyze further the current Heart Disease Data Set provided by the UCI Machine Learning Repository. We applied logistic regression to the Heart Disease Dataset. The dataset contains 303 instances and 14 features. We preprocessed the dataset, removing missing values and performing feature scaling. We then trained and tested the logistic regression model using k-fold cross-validation. Our results showed that the model achieved an accuracy of 83.77% in predicting heart disease presence. The model's precision, recall, and F1-score were 81.2%, 84.1%, and 83.8%, respectively. Our findings demonstrate the potential of logistic regression in predicting heart disease presence and provide insights into improving early detection and management of the disease.
When: Friday, April 28, 2023, at 3:00pm in PB 11
Presenter: Gabriel Chavez (Mathematics Master's Student)
Title: Pedagogy: Its effects on non-cognitive outcomes for first semester calculus 1 students
Abstract: We examine first-semester calculus pedagogies at Fresno State and their implications for STEM outcomes, particularly for first-generation, low-income, and underrepresented minority (URM) students. Fresno State reformed its traditional calculus curriculum to address achievement gaps. Our analytical framework evaluates the impact of pedagogical approaches on non-cognitive achievements, emphasizing cooperative learning's role in fostering confidence and self-efficacy. Using a mixed-methods approach, we analyze student surveys, interviews, and observations, incorporating an intersectional lens to understand URM students' diverse experiences. Our findings indicate significant differences in non-cognitive achievements between traditional and reformed calculus instruction, suggesting that reformed teaching practices can enhance students' confidence, self-efficacy, and STEM success.
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.
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.