# GAUSS (Graduate and Undergraduate Students Seminar)

## Upcoming Seminars

More to come in Fall 2019!

## Past Seminars

**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.**