Colloquium in Mathematics and Computer Science I & II

Mathematics and Computer Science Colloquium

Opportunities in Semi
Ramon Olavarria
Sr. IT Director
IT
KLA
Milpitas, CA

KLA is a leader in Optical and Electron Beam Inspection. Our customers, Samsung, Intel, Micron, Global Foundry, just to name a few partner with KLA to help drive the next generation of microchips We're at the nexus of electron and photon optics, sensor technology and artificial intelligence. From raw wafer to next-gen chip to world-altering idea, we help enable what's next. KLA is proud to be part of the most significant technological breakthroughs. Virtually no laptop, smartphone, wearable device, voice-controlled gadget, flexible screen, VR device or smart car would have made it into your hands without us. I will discuss what KLA does and how Mathmatics and Computer Science graduates come and make a difference at KLA.

Palenske 227
3:30 PM

All are welcome!

Mathematics and Computer Science Colloquium

Function Field Arithmetic: Working with Analogues
Erik Davis
Texas A&M University
College Station, TX

In studying arithmetic of various kinds, one is often faced with fairly abstract settings. In order to grapple with these settings, it is often useful to first understand a similar story that already has some development and then return to the new setting with an analogy in mind. In this talk, I will provide some examples of this from the setting of function fields.

Palenske 227
3:30 PM

All are welcome!

Mathematics and Computer Science Colloquium

Careers in Mathematics and Computer Science
David A. Reimann
Professor
Albion College
Albion, MI, USA

A degree in mathematics or computer science is excellent preparation for employment in areas such as teaching, actuarial science, software development, engineering, and finance. Come learn about career opportunities awaiting you after graduation.

Palenske 227
3:30 PM

All are welcome!

Mathematics and Computer Science Colloquium

The Top-Bottom Shuffle and Two Related Card Tricks
Stanley Ryan Huddy
Associate Professor of Mathematics
Fairleigh Dickinson University
Teaneck, New Jersey

Card tricks are often a combination of mathematics and sleight of hand. For those with a lack of dexterity, I'll explain two self-working tricks that are purely mathematical. Both tricks rely on the Top-Bottom Shuffle. I will develop the mathematics behind the shuffle and prove why each trick works.

Palenske 227
3:30 PM

All are welcome!

Mathematics and Computer Science Colloquium

Estimating Population Size using Capture-Recapture Data
Paul Anderson
Dr. Paul Anderson
Mathematics and Computer Science
Albion College
Albion, Michigan

Capture-recapture is a sampling design that is used to estimate the size of animal populations in a wilderness. A random sample of $M$ animals is captured, and the animals are tagged and released. At a later time, another random sample of $n$ animals will be recaptured and the number of tagged animals $X$ is recorded.

Given values of $M$, $n$, and $X$, we will estimate the population size $N$ using the hypergeometric probability distribution. We will then be able to approximate the hypergeometric distribution with the normal distribution. From the normal distribution, we derive a third-degree polynomial that provides a confidence interval for the unknown $N$.

To illustrate our method, we will break into groups. Each group will estimate the number of black beans in a bowl. The estimate will be in the form of a confidence interval.

Palenske 227
3:30 PM

All are welcome!

Mathematics and Computer Science Colloquium

Pizza and Pamphlets plus Pi Day Extravaganza
Mark Bollman
Professor of Mathematics and Chair
Albion College
Albion, Michigan

Pizza and Pamphlets is the event where the Mathematics and Computer Science Department provides information about spring courses in Mathematics and Computer Science. All Math majors/minors, Computer Science majors/minors, Math/Physics majors, Math/Econ majors, prospective majors, and friends of the department are invited to join us. The event will be held at 3:30 pm in Palenske 227/229. Bring your friends; bring your questions; bring your schedule. We will also provide pizza and pop!

We will also celebrate Pi Day with a selection of pie!

Palenske 227
3:30 PM

All are welcome!

Mathematics and Computer Science Colloquium

Mathematics, music, and metaphor
Timothy L. Clark
Associate Professor and Chair
Adrian College
Adrian, Michigan

How does one go about research in mathematics? More importantly, what is the point? In this talk, I will share my perspective on these questions, motivated by some examples from my own experience and research activities. In particular, I will attempt to articulate my thoughts on the use of metaphorical and figurative reasoning in the pursuit of mathematical understanding. Once established, we will put these ideas into practice by examining a result from mathematical music theory related to the study of musical gestures and their topological characterization in a convenient category of spaces.

Palenske 227
4:00 PM

All are welcome!

Mathematics and Computer Science Colloquium

Functional Regression in Estimating Post-Traumatic Stress Symptoms Trajectories
Methsarani Premathilaka
Visiting Assistant Professor
Wake Forest University
Winston-Salem, North Carolina

We provide a new approach to analyzing sparse irregularly spaced longitudinal data to study the early development of Post Traumatic Stress Disorder. In our study, we aimed to demonstrate that Functional Data Analysis is a potentially superior tool for analyzing longitudinal trajectories of PTSD symptoms. It has the flexibility to capture the changes in nonlinear patterns and can be used to examine the longitudinal interactions of PTSD symptoms with behavioral, brain structure changes, and other factors. We use data from two existing longitudinal studies and combine together to create a large database. The individual trajectories of PTSD symptoms, depression, and cortical thickness were estimated using Functional Principal component Analysis. Association among these measures was studied using functional regression analysis. Our findings show that the FDA is a powerful tool to study the longitudinal trajectories of the early development of PTSD.

Palenske 227
4:00 PM

All are welcome!

Mathematics and Computer Science Colloquium

Fake It Till You Make It: Circuits of Pseudoflow Polyhedra
Angela Morrison
Mrs.
University of Colorado Denver
Denver, Colorado

There is a wealth of combinatorial algorithms for classical min-cost flow problems and their simpler variants like max flow or shortest-path problems. It is well-known that several of these algorithms are intimately related to the Simplex method and the more general circuit augmentation schemes. Prime examples are the network Simplex method, a refinement of the primal Simplex method, and (min-mean) cycle canceling, which corresponds to a (steepest-descent) circuit augmentation scheme over the underlying polyhedron. We are interested in deepening and expanding the understanding of the close relationship between circuit augmentation and combinatorial network flows algorithms. To this end, we generalize from the consideration of primal or dual feasible flows to the so-called pseudoflows, which allow for a violation of flow balance. We introduce what are called 'pseudoflow polyhedra', in which slack variables are used to quantify this violation, and characterize their circuits. This enables us to study various network flows algorithms in view of the walks that they trace in these polyhedra, and in view of the pivot rules used to choose the steps.

Palenske 227
3:30 PM

All are welcome!

Mathematics and Computer Science Colloquium

Unraveling Hidden Patterns with Topological Data Analysis (TDA)
Elena Wang
PhD Candidate
Michigan State University
East Lansing, Michigan

Topology, akin to geometry, delves into the study of the shapes and structures of mathematical spaces, ranging from simple surfaces to intricate collections of functions and objects. In recent years, these foundational concepts have extended beyond pure mathematics to address practical problems in data science, influencing diverse areas such as chemistry, neuroscience, and robotics. This talk aims to demystify the core techniques of Topological Data Analysis (TDA), such as persistent homology, and illustrate their significance through applications in machine learning, time series analysis, and computational biology. We will explore how TDA provides unique insights into data structuring and analysis, offering solutions to complex problems. Additionally, I will leave the audience with some current challenges and open questions within the field as food for thought.

Palenske 227
3:30 PM

All are welcome!

Mathematics and Computer Science Colloquium

Decoding Ultrahigh-Power Lasers
Chengyong Feng
University of Rochester
Rochester, NY

Lasers have applications in many areas, such as communication, manufacturing, and medicine, that are closely related to our daily lives. Lasers also become indispensable tools in scientific research, for example, in creating conditions with extreme temperature and pressure for studying Laboratory Astrophysics and Planetary Physics.

One of the forefronts in laser R&D is the development of ultrahigh-power lasers with peak power exceeding 10 petawatts (PW) or 10×10¹⁵ watts. The backbone technology that enables such high laser power is the so-called chirped pulse amplification (CPA), which was originally demonstrated at the University of Rochester's Laboratory for Laser Energetics (LLE) in 1985 and garnered the 2018 Nobel Prize in Physics.

In this talk, I will review the lasers as electromagnetic waves, construct lasers using fundamental mathematical functions — the sinusoidal functions, explain the necessity of using CPA technology in building high-power lasers, and decode CPA using coherent combination of sinusoidal functions with varying phases. I will then briefly show three recent high-power lasers at LLE with increasing peak power and physical scale. The latest is a laser project called NSF-OPAL that was funded by the National Science Foundation in 2023 to design a 2×25 PW laser facility. Once built, NSF-OPAL will become the most powerful laser in the world.

Palenske 227
3:30 PM

All are welcome!

Mathematics and Computer Science Colloquium

The Fundamentals of Finite Markov Chains through Applications
Michael A. Jones
Managing and Associate Editor
Mathematical Reviews
American Mathematical Society
Ann Arbor, MI

A Markov chain is a probabilistic model that generates a sequence of outcomes such that the probability of the next term in the sequence only depends on the current term. Even though the study of finite Markov chains applies elementary ideas from linear algebra and probability theory, the topic is rarely taught in either class. This is a shame because the ideas are straightforward and the applications are varied, compelling, and accessible. In this talk, the fundamentals of Markov chains—including the fundamental matrix, regular chains, absorption times, etc.—will be introduced through applications including the Super Bowl box pool, the Penney Ante game (made popular by Martin Gardner), the television game show The Chase, and Chutes and Ladders.

Palenske 227
3:30 PM

All are welcome!

Mathematics and Computer Science Colloquium

Senior Majors
Albion College
Albion, Michigan

Presentations by senior mathematics and computer science majors.

Palenske 227
3:30 PM

All are welcome!