Department of Mathematics
Colloquium Series
Upcoming Colloquia
Thursday, March 30, 2023 - Dr. Melissa Zhang (postdoc at UC Davis)
At 12 PM in PB 390
Title: Using Algebra to Study the 4D Behavior of Knots
Abstract: A knot is a closed loop of string in 3-space. When subject to gentle wiggling and deforming, a knot does not lose its most inherent properties, making it a foundational object in many areas of topology. The simultaneous visual intuitiveness and rich diversity of knots allows them to also serve as bookkeeping tools for many other fields, including statistical mechanics, algebraic combinatorics, quantum computing, and many more.
Given two random pictures of complicated knots, it would be near impossible for a human to immediately determine whether the knots are different. For tasks like this, we use knot invariants, which assign diagrams of knots to some other mathematical object that we understand better. For instance, a famous knot invariant called the Jones polynomial assigns to each knot diagram a (Laurent) polynomial, and if given two different diagrams of the same knot, it will produce the same polynomial.
Knot invariants like the Jones polynomial are useful not only for telling knots apart but also for classifying them based on their similarities. A more recent enhancement of the Jones polynomial called Khovanov homology assigns a more complex algebraic object to a knot diagram. By studying knots through their Khovanov homology, one can now capture relationships between knots, or more precisely, the evolution of knots throughout 4D spacetime.
In this talk, we will get a taste of how Khovanov homology extends the Jones polynomial to the fourth dimension, and explore several ways the 4D behavior of knots makes them even more interesting.
Short Bio: Melissa Zhang is currently a Krener Assistant Professor at UC Davis. Previously, she was a postdoc at MSRI/SLMath, and the University of Georgia. She earned her PhD at Boston College under the supervision of her advisors Eli Grigsby and David Treumann. She is a low-dimensional topologist who studies visualizations of physical objects like knots, 3D spaces with portals, as well as 4D analogues of knots. In practice, if you ever watch her doing research, she is probably doing one of the following activities: (1) drawing pictures, (2) collaborating with friends, (3) trying to write down her proofs carefully, or (4) thinking through arguments using linear algebra.
She's always loved science and math growing up, but her pure math career really began when she took her first proof-based course in college and loved it! She also enjoys singing, knitting, hiking, and playing with her pet rats.
Recent Colloquia
Friday, March 24, 2023 - Dr. Scott Mitchell (Sandia Lab)
At 9 AM via Zoom (Register in advance at https://us06web.zoom.us/j/83723613079)
Title: Computing geometry as a mathematician in an engineering laboratory
Abstract: Geometry is all around us. Sandia creates physical objects with physical shape, and
we need to explore the abstract high-dimensional spaces that describe the variety
of environmental conditions these objects might encounter. They
must always "work" when we want them to, and never "work" when we don't! I study computational
geometry, which is the math and algorithms for calculating geometric quantities of
objects, or creating new objects with prescribed geometry. My favorite work is joining
up with people with a different background from me, such as mechanical engineering,
optimization, uncertainty quantification, geophysics, or data sciences. As a mathematician,
they often ask me *how* to solve some problem they are stuck on. Instead, I ask them
*why* they want to solve it and usually end up redefining their problem so it is easy
to solve. My favorite problems involve the interplay between continuous shapes and
the discrete connections binding them together. I study triangular and cubical meshes,
and how to optimize them for increased simulation accuracy. I also study point-sampling
of abstract spaces, and computational topology to characterize the structure of fragments.
I'll describe my journey from my family to the labs, what it's like to work there,
and work with the international research community. I'll mention a few research highlights
from my nearly 30 years at Sandia and 75 publications. The talk is intended to be
accessible to STEM undergraduates.
Short Bio: Scott A. Mitchell received a B.S in Applied Math, Engineering & Physics from the University of Wisconsin-Madison in 1988. He received an M.S. (1991) and Ph.D. (1993) in Applied Math from Cornell University. Since Oct 1992 he has been at Sandia National Laboratories. He researched triangular and tetrahedral meshing algorithms via a computational geometry approach from 1992-1993. He was part of the Cubit project, doing mesh generation R& D from 1993-2000, and project leadership from 2000-2002. He managed the Optimization and Uncertainty Estimation department from 2002-2007. He served on Sandia's LDRD (internal research program) team and NNSA's ASC program. He moved on to technical work in 2007. He published about 75 papers, and served on the program committee for the International Meshing Roundtable and Symposium on Computational Geometry He is a member of SIAM and ACM.
Friday, February 24, 2023 - Dr. Kelly Moran (Los Alamos National Lab)
At 9 AM via Zoom (Register at https://us06web.zoom.us/meeting/register/tZAofuqprTsvE9AA2pUXzuSlt6aAm6bvdWMS)
Title: Understanding the universe on large scales
Abstract: In this seminar, I introduce myself and my background and talk about a cosmology project
I've been working on for a little over a year. You'll hear about how when I first
started working at Los Alamos National Lab (LANL) I knew nothing about statistics,
compared to now when I have a PhD in it! In a similar vein, you'll hear that when
I first started working on this project I knew nothing about cosmology, but now I
know enough to be useful. Cosmology aims to understand the universe on large scales.
In order to maximally extract information from modern cosmological surveys, matching
theoretical predictions are 39 needed. At low redshifts cosmological simulations are
the main way of getting predictions, but their computational cost makes it impossible
to run very large ensembles. We built an emulator for the matter power spectrum based
on the Mira-Titan Universe simulation suite that is designed to be useful for
cosmological inference studies on a range of cosmological probes. It is more accurate
(at the 2-3% level) than competing methods, and covers a larger range of cosmological
parameters.
Short Bio: Dr. Moran works on developing, analyzing, and visualizing Bayesian statistical models
across varied applications such as global and environmental health, cosmology, and
space physics. She has experience in developing novel methods for probabilistic dimension
reduction and fast Gaussian process approximation. She first joined Los Alamos National
Laboratory as a post-baccalaureate student with the Information Systems and Modeling
(A-1) group, returned throughout graduate school to work with the
Statistical Sciences (CCS-6) group, and hired on with CCS-6 as a staff scientist in
2021. She enjoys being outside, blues and fusion dancing, playing the oboe, and hanging
out with her two large orange cats.
Celebrating Women’s History Month
Friday, March 3, 2023 - Dr. Catherine Cavagnaro (Sewanee: The University of the South)
At 11 AM in SII 206
Title: Mathematical Models for Aircraft Longitudinal Motion
Abstract: Longitudinal motion for an aircraft refers to forward and vertical translational motion as well as rotation about the lateral axis. We will present and explore mathematical models for such motion and extract techniques pilots can use to more safely fly their aircraft.
Short Bio: In addition to teaching mathematics at Sewanee, Catherine Cavagnaro holds FAA Flight Instructor and Airline Transport Pilot certificates. She teaches aerobatics at the airport on campus and is a monthly columnist for AOPA Pilot Magazine. In 2018 Catherine was inducted into the Tennessee Aviation Hall of Fame and in 2022, she was inducted into the National Flight Instructor Hall of Fame. She enjoys flying with her two sons around the United States and delights in finding mathematical applications within aviation.
Friday, February 3, 2023 - Dr. Gi-Sang Cheon, Sungkyunkwan University
At 10 AM in PB 138
Title: Introduction to Riordan arrays and applications
Abstract: Enumeration problems in combinatorics arise in many areas of mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Although primarily concerned with finite systems, some combinatorial questions and techniques can be extended to an infinite (specifically, countable) but discrete setting. A Riordan array (or Riordan matrix) is an infinite lower triangular matrix encoding the coefficients of certain sequences of power series. Such an array can be regarded as a vast generalization of Pascal’s triangle. These concepts lead to an elegant, unified, and fruitful approach for dealing with a host of enumerative problems.
Short Bio: Gi-Sang Cheon is a Korean mathematician working in combinatorial matrix theory, enumerative combinatorics, and Riordan group theory. He is currently the director of the Applied algebra and Optimization Research Center (AORC) , SRC-NRF of Korea since 2016. He is also a professor of the Department of Mathematics at Sungkyunkwan University. He received his Ph.D. from Sungkyunkwan University in Feb 1991. His research interests include linear and multilinear algebra, graph theory, and their applications.
Thursday, December 1, 2022 - William Godoy, PhD (Oak Ridge National Laboratory (ORNL))
To attend the talk you will first need to register in advance at https://us06web.zoom.us/j/88406041576
Title: Pursuing graduate school and career paths for PhDs
Abstract: In this presentation we will talk about career paths for those planning to pursue a graduate school degree. We will provide exposure to the audience from my experiences on different career paths environments: academia, national labs and industry. In particular, we would point out the importance of having a diverse network for collaboration, being part of a scientific community, and the role of professional societies. We will also discuss the different kind of expectations as people progress in their professional career levels and uptake on early, mid and senior roles. Overall, we hope students will get exposure to these topics to get a grasp of the landscape in science and help them navigate these environments.
Short Bio: Dr. William F Godoy joined Oak Ridge National Laboratory in 2016, currently a Senior
Computer Scientist in the Computational Science and Mathematics Division. A native
of Peru, his background is in Mechanical Engineering with a strong research and development
focus on the computational aspects of large-scale scientific modeling and simulation
using high performance
computing (HPC) He obtained his PhD in 2009 from the University at Buffalo, The State
University of New York. Prior experiences include a Senior Software Engineer position
at Intel Corporation, 2012-2016, and a postdoctoral fellow at NASA Langley Research
Center, 2009-2012. https://www.ornl.gov/staff-profile/william-f-godoy
Thursday, November 3, 2022 - Earvin Balderama, Ph.D. (Fresno State)
By Zoom at 12 PM
Title: Statistical Models for Count Data
Abstract: Count data are a type of data that takes on non-negative integer values {0, 1, 2, ...}. The Poisson and negative binomial distributions are commonly used as the basis in a generalized linear model for such data. The negative binomial is used in situations where the Poisson fit is inadequate due to over-dispersion. When there is an excess amount of zeros in the data, zero-inflated models and hurdle models are used, again typically specified by Poisson and negative binomial. What if negative binomial is still inadequate? In this talk, I will discuss the double-hurdle model, an extension of the single-hurdle model, to describe count data that contain both an excessive amount of zeros and some extremely large counts that cause so much over-dispersion that even a negative binomial specification is inadequate. The double-hurdle model was applied to counts of marine birds observed along the US Atlantic coast. A Bayesian MCMC framework was used for estimation and validation. An R package, hurdlr, was created to implement hurdle and double hurdle models to zero-inflated data.
Friday, October 28, 2022 - Nathan Urban, Ph.D. (Brookhaven National Laboratory (BNL))
By Zoom at 9 AM
Title: PROJECTING THE FUTURE: QUANTIFYING UNCERTAINTIES IN HOW THE CLIMATE WILL CHANGE
Abstract: As carbon dioxide emissions to the atmosphere continue from fossil fuel consumption, the Earth's climate will change considerably over the course of this century due to the resulting greenhouse effect. Societies and ecosystems will feel these global changes in the form of extreme weather, recurrent flooding and droughts, and other regional impacts. But how certain are we in projections about the distant future? Every prediction of a physical theory comes with error bars arising from limitations in data and approximations that are made for the sake of computational tractability. The scientific question is not whether the climate will change, but how likely it is to change by a given amount. This talk will discuss at a conceptual level the general mathematical formalism of statistical uncertainty quantification, and how it is being applied within the U.S. Department of Energy and other research institutions to estimate the plausible range of possible climate futures. The mathematical methods discussed may include Bayesian parameter estimation for nonlinear regression, Monte Carlo sampling, sensitivity analysis, model averaging, and surrogate modeling or emulation of expensive computer simulations. Applications may include probabilistic predictions of global warming and climate feedbacks, sea level rise from Antarctic ice sheet disintegration, and coastal flooding, among others. As time permits, I will also discuss educational training and career paths into this research field at the forefront of interdisciplinary science.
Short Bio: Dr. Nathan Urban leads the Applied Mathematics group in the Computational Science Initiative at Brookhaven National Laboratory, on Long Island, New York. He received undergraduate degrees in physics, computer science, and mathematics from Virginia Tech, and a Ph.D. and M.Ed. in physics (computational statistical mechanics) from Penn State. After graduating, he moved into climate uncertainty quantification with postdoctoral appointments at Penn State and Princeton, and a staff position at Los Alamos National Laboratory. He received a DOE Office of Science Early Career Research award for multi-model climate uncertainties, and has led major projects involving coastal resilience planning under uncertainty and "in-situ" methods for embedding scalable statistical inference algorithms within exascale simulations. At Brookhaven he develops methodologies for uncertainty quantification, decision making under uncertainty and optimal experimental design, model reduction, scientific machine learning, and integrated computational frameworks for decision support, applied to problems in climate science, biomedicine, materials science, and others.
Friday, October 7, 2022 - Dr. Mario Bencomo
In PB 013 at 3 PM
Title: Topics in inverse problems
Abstract: Inverse problems are a classification of mathematical problems in engineering and science that involve estimating model parameters/inputs relative to a “forward/direct” problem. In this talk I will present several examples of inverse problems to elucidate the definition and highlight typical mathematical challenges. I will also discuss in depth applications in the field of exploration seismology where such inverse problems require mathematical tools from numerical optimization and differential equations.
Short Bio: Mario J. Bencomo joined the Department of Mathematics at Fresno State as an Assistant Professor this Fall semester. Prior to coming to California, he was a Pfeiffer Postdoctoral instructor at Rice University, in the Department of Computational Applied Mathematics and Operations Research (CMOR), where he received his Ph.D. in 2017. His research interests include numerical methods for wave propagation problems, inverse problems, optimal control with a focus on nonlinear conservation laws.
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.