Department of Mathematics

# Colloquium Series

## Upcoming Colloquia

**Friday, December 3, 2021 - Jennifer Elder**

**By Zoom at 9 AM**

**Title: **Graphs of Sets of Reduced Words

**Abstract: **Any permutation in the finite symmetric group can be written as a product of simple
transpositions of the form (i i+1). We use these transpositions to represent a permutation
as a reduced word. In this talk, we will look at examples of permutations and the
sets of reduced words we can generate. We will look at how these sets can produce
an associated graph, and cover new results on breaking the graphs into subgraphs and
counting the number of edges in each graph.

**Short Bio:** Jennifer Elder attended Fresno State for her Bachelor’s and Master’s degrees in
Mathematics, graduating in 2014 and 2016 respectively. During her time as an undergraduate,
she was a Fresno State Tensor Women Scholar, working in knot theory research with
Elaina Aceves under the supervision of Carmen Caprau. She also worked with Oscar Vega
on expanding the research on GRIM, a combinatorial game on graphs, and was one of
the original student organizers and activity leaders for Fresno State’s Sonia Kovalevsky
Mathematics Day. During the Master’s program, Jennifer worked on “Generalizing the
Futurama Theorem,” which was research on products of permutations in the symmetric
group. This project also gave her the best answer to the question that plagues theoretical
mathematicians: “what are the applications of your research?” Defeating supervillains,
thank you very much. She graduated with honors and earned the Mathematics Department
Outstanding Thesis award. After leaving Fresno State, Jennifer went to Arizona State
University for her Doctorate, which she finished in the Summer of 2021. Her dissertation
was on permutations in the symmetric group in the field of algebraic combinatorics
under the supervision of Susanna Fishel. During her time in Arizona, Jennifervolunteered
yearly as an activity leader and guest panelist at ASU’s Math Day and Sonia Kovalevsky
Day. She worked on the leadership team for the ASU Association for Women in Mathematics
Student Chapter, first in the position of Secretary and then as President.

Jennifer is now a Visiting Professor of Mathematics at Rockhurst University in Kansas
City. She intends to stay in academia, continuing her research and working on curriculum
and course structures to create a more equitable and inclusive environment for underrepresented
students in STEM.

**Recent Colloquia**

**Friday, November 5, 2021 - Andrew Gillette, Ph.D. (Lawrence Livermore National Laboratory)**

**By Zoom at 11 AM**

**Title:** Why are Mathematicians Jumping on the Machine Learning Bandwagon?

**Abstract:** “Scientific machine learning” is a catch-all term for many current and future directions
of computational science research, especially at national laboratories. What can mathematicians
bring to this very code-centric field? A lot, it turns out. Neural networks are now
thought of not only as a tool for modeling physical phenomena, but also as classes
of functions, similar to solution spaces for partial differential equations. Mathematicians
are well-poised to leverage results from numerical analysis and computational geometry
to aid in the rigorous design of neural networks for scientific studies. In this seminar,
I will speak in detail about my research using Delaunay triangulations (a technique
dating to the 1930s) to analyze sampling and training procedures for neural networks.
Simple examples in 2D will motivate the approach, followed by extension to dimensions
beyond the reach of classical computational geometry methods. I will present applications
of these tools in the context of multiple lab-supported research programs.

**Friday, October 29, 2021 - Elaina Aceves (University of Iowa)**

**By Zoom at 9 AM**

**Title:** *Introduction to Train Tracks*

**Abstract:** In this talk, I will focus on 3-braids which are isomorphic to the mapping class
group of a 3-punctured disk. Using this interpretation, I will introduce train tracks
which can be used to measure the twisting of the braid, maximal splitting sequences,
and Agol cycles. In the latter half of the talk, I will discuss my current research
which is about detecting the conjugacy class of pseudo-Anosov 3-braids admitting a
non-degenerate flype by using Agol cycles.

**Short Bio: **Elaina Aceves is originally from Tulare CA and had the great opportunity to attend
Fresno State under the Smittcamp Family Honors College Scholarship. While at Fresno State, she was introduced to undergraduate
mathematics research by Tamás Forgács and decided to change her major from engineering
to mathematics. During the summer of 2012, Elaina participated in an REU in geometry
with Ashley Klahr and David Heywood under the advisement of Oscar Vega. As a Fresno
State Tensor Women Scholar, she also worked in knot theory research with Jennifer
Elder under the advisement of Carmen Caprau. Elaina’s undergraduate research would
lead to two published papers, one in the Journal of Geometry and one in the Rose-Hulman
Undergraduate Mathematics Journal. After obtaining her bachelor’s degree in mathematics
in 2014, Carmen would become her master’s thesis advisor. Carmen supported Elaina
to attend multiple mathematics conferences and become an activity leader in Sonia
Kovalevsky Day. Elaina would graduate with her masters in 2016 and earn the Department
of Mathematics’ Outstanding Graduate Student award. Her master’s thesis would lead
to another published paper in the Journal of Knot Theory and its Ramifications. After
graduating, Elaina went to the University of Iowa to earn her Mathematics PhD. During
her first years at the University of Iowa, Elaina earned the Graduate Assistance in
Areas of National Need Fellowship and became an Alfred P. Sloan scholar. She also
earned the prestigious Ford Foundation Predoctoral Fellowship which supported her
last three years of graduate study. While at Iowa, she has continued to promote females
in mathematics by participating in Sonia Kovalevsky Day and outreach activities like
Topology Kids Club. Elaina has also been a mentor and organizer in the student-run
Directed Reading Program which seeks to involve undergraduates in the mathematical
community and provide a place to study an interesting topic in mathematics. Under
the advisement of Keiko Kawamuro, Elaina has continued her research in topology and
plans to graduate with her PhD in May 2022. She hopes to attain an academic position
where she can promote undergraduate research and continue to support underrepresented
students in mathematics.

**Friday, September 24, 2021 - **Rick Archibald Ph.D. (Oak Ridge National Laboratory)

**By Zoom at 9 AM**

**Title: ***A Path to Applied Mathematics at the DOE*

**Abstract: **This presentation will highlight different applied mathematical research that is supported
at the laboratory complex at the Department of Energy (DOE). It will focus on data
analytics and provide information on various programs designed to foster engagement
with the DOE.

**Short Bio:** Dr. Archibald is group leader of Data Analysis and Machine Learning Group Oak Ridge
National Laboratory and he is also the data analytics lead for the SciDAC DOE institute
FASTMath. He received Ph.D. in Mathematics from Arizona State University in 2002,
with Anne Gelb that is currently in the Department of Mathematics, at Dartmouth College.
He works in the Computational and Applied Mathematics Group at Oak Ridge National
Laboratory. His research interests lie in data reconstruction and analysis, high order
edge detection, large scale optimization, time integration, and uncertainty quantification.

Presenter Website: https://www.ornl.gov/staff-profile/richard-k-archibald

**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.**