# Seminar Series

## Upcoming Seminars

**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: **

### Recent Seminars

**FALL 2019**

**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: **

** **

**SPRING 2019**

**Date and Time: **Friday, April 5, 2019, at 9 AM

**Location:** PB 138

**Title: ***On the Non-hypercyclicity of Scalar Type Spectral Operators and Collections of Their
Exponentials*

**Speaker: **Marat Markin

**Abstract: **We give a straightforward proof of the non-hypercyclicity of scalar type spectral operators
and certain collections of their exponentials. The important particular case of normal
operators follows immediately.

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

**Location: **PB 138

**Title: ***Modified commutation relationships from the Berry-Keating program*

**Speaker: **Michael Bishop

**Abstract: **Current approaches to quantum gravity suggest there should be a modification of the
standard quantum mechanical commutator, [^x; ^p] = i. Typical modifications are phenomenological
and designed to result in a minimal length scale. As a motivating principle for the
modification of the position and momentum commutator, we assume the validity of a
version of the Bender-Brody-Muller symmetry operator in their suggestive approach
to the Riemann hypothesis. We arrive at a family of modified position and momentum
operators, and their associated commutator, which lead to a minimal length scale.
Additionally, this larger family generalizes the Bender-Brody-Muller approach.

**FALL 2018**

** Date and Time: **Friday, November 20, 2018, at 11 AM

**Location:** PB 136

**Title: ***On Hypercyclicity for Unbounded Linear Operator*

** Speaker: **Marat Markin

**Abstract:**

** Date and Time: **Friday, November 2, 2018, at 9 AM

**Location: **PB 136

**Title: ***The Quantum Harmonic Oscillator and a Step Toward GNS Construction*

**Speaker: **Michael Bishop

** Abstract: **The quantum harmonic oscillator is a standard example of a quantum variation of a
classical system. It inspires many of the elements of quantum field theory. I will
introduce this model along with the ladder method for solving for all the energy eigenvalues
and associated eigenfunctions. From there, I will introduce the Gelfand-Naimark-Segal
construction which is a method to recover a Hilbert space of states from a Banach
Algebra. We will return to the oscillator and apply a similar method to this specific
model which, as far as I can tell, has not been done. This is preliminary work with
Gerardo Munoz from the Physics department.

**Date and Time:** Friday, October 26, 2018, at 9 AM

**Location:** PB 136

**Title: ***A Space-Time Double-Hurdle for Marine Bird Count Data *

**Speaker:** Earvin Balderama

**Abstract: **The spatial distribution and relative abundance of marine birds along the US Northeast
and Mid-Atlantic coastlines are of special interest to ocean planners. However, marine
bird count data often exhibit excessive zero-inflation and over-dispersion. Modeling
of such data typically involves a truncation or censoring technique to avoid the extremely
large counts. Our modeling effort incorporates a spatial-temporal double-hurdle model
specifically tailored to look at extreme abundances, which is especially important
for assessing potential risks of offshore activities to sea ducks and other highly
aggregative species. The double-hurdle model includes negative binomial and generalized
Pareto distribution components to handle the extreme right tails and is compared to
several single-hurdle specifications using Bayesian model selection criterions. Spatial
heterogeneity is modeled using a conditional autoregressive (CAR) prior, and a Fourier
basis was used for seasonal variation. Model parameters are estimated in a Bayesian
hierarchical framework, using an MCMC algorithm with auto-tune parameters, all written
and run in R. We demonstrate our model by creating predictive maps that show areas
of high probability of aggregation and persistence for several species of marine bird.

**Date and Time: **Friday,** **October 12, 2018, at 9 AM

**Title: ***Investigating the Gerchberg-Saxton algorithm: Some updates*

** Speaker: **Comlan de Souza

**Date and Time: **Friday, September 28, 2018, at 9 AM

**Location: **PB 136

**Title: ***The sum of polynomials with three recurrence*

**Speaker: **Khang Tran

**Abstract: **

**Date and Time: **Friday, September 14, 2018, at 9 AM

**Location: **PB 136

**Title: ***Deep Learning - Motivation and Applications*

**Speaker: **Mario Banuelos

**Abstract: **As a state-of-the-art machine learning tool, deep learning is often viewed as a black-box
tool for applications such as image classification, speech recognition, and signal
processing. In this talk, we will explore how linear and logistic regression can be
viewed as a neural network mathematically as well as an overview of the different
optimization techniques used to minimize error. An important part of optimizing performance
in a deep learning model is the choice of an activation function since activation
functions allow deep learning models to approximate functions of complex, nonlinear
data.

To further explore this idea, we study the importance of choosing an activation function. We designed and carried out experiments to measure the effectiveness of specific activation functions in multiple architectures. We propose a two-parameter, trainable activation function which we call TAct. We briefly explore the performance of Taylor Series approximations of TAct fitted to popular activation functions, including Rectified Linear Unit (ReLU), in a convolutional neural network (CNN) to reconstruct noisy representations of handwritten digits.

**Date and Time: **Friday, August 31, 2018, at 9 AM

**Location: **PB 136

**Title: ***Eigenvalue techniques in graph theory and* combinatorics

**Speaker: **Morgan Rodgers

**Abstract: **When we are dealing with a finite mathematical structure, such as a graph, a finite
geometry, or a collection of subsets from some fixed set, it is often possible to
encode relevant information about the structure under consideration in the form of
a matrix. This opens up the possibility of applying linear algebra techniques to the
matrix to assist in studying properties of the related structure. In particular, looking
at the eigenvalues and eigenspaces of a matrix related to a mathematical structure
often provides deep information about the structure; this is often loosely referred
to as applying “eigenvalue techniques” to study the structure in question.

One common example of the application of eigenvalue techniques arises in graph theory. The adjacency matrix of a graph is a 0-1 graph that contains all of the information about which vertices are joined by edges. While a graph is not completely determined by the eigenvalues and multiplicities of this matrix, we can obtain information about whether the graph is regular, the diameter of the graph, even strong bounds on the size of the largest cliques and independent sets.

In this talk, we will look at some different settings where eigenvalue techniques have been used to solve difficult combinatorial problems.

**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.**