Categorical dynamics on stable module categories

Topological entropy is a measure of the complexity of a continuous self-map of a compact topological space. Categorical entropy generalizes this measure to exact endofunctors of triangulated categories. In this work we ask: How can categorical entropy serve to quantify growth in stable homotopy theory, and how can the methods of stable homotopy theory aid in understanding and computing categorical entropy? We show that the categorical polynomial entropy of a twist functor on the stable module category of a finite connected graded Hopf algebra A over a field k recovers one less than the Krull dimension of H*(A;k), generalizing a computation of Fan, Fu, and Ouchi. Along the way, we will see how a stable homotopy theoretic-perspective permits us to make this refinement.

Factoring the Burnside Adams Operation through the Power Operation

Within representation theory, it's well known that the Adams operation can be factored through the power operation. Similar factorizations exist for some other cohomology theories. It is not known for the Burnside ring. Our primary goal is to describe such a factorization for the Burnside ring in certain cases. We begin by recalling the Burnside ring and these operations, then observing a theorem by Gay, Morris, and Morris which describes the Adams operation, and finally, describing the three major steps of the proof.

Analysis and PDE Seminar Spring 2023 schedule details are available here.

Mathematics Alumni Day at the University of Kentucky brings together students, faculty, alumni, and friends of the Department of Mathematics to celebrate the accomplishments of our alumni.

Date and location

Date: Friday, April 1, 2022

Location: CB 122

Time: 2:00 – 5:30 p.m.

Speakers / Presenters

Liam Solus, Kristen Barnard, Stephen Sturgeon

Summary

Three UK Math Department alumni will return to UK to share their journey with current faculty, math graduate students, and undergraduate students.

Name: Liam Solus, KTH Stockholm (Zoom)

Title: On the Road to Tenure in Research Academics 

Abstract: A Ph.D. in mathmatics opens up a variety of different career paths in today's society, including lucrative industry positions, professorships in undergraduate teaching fucused-collges as well as professorships in Ph.D.-granting programs. While each of these career-paths naturally intersects with the others, success in one direction often means prioritizing certain activities during your time as a Ph.D. Student. I will refect on my experience and the choices I made as I pursued a tenure-track position within a Ph.D. granting mathematics program, starting from my time as a Ph.D. student at the University of Kentucky. We will discuss the importance of networking, grant writing, leadership and teaching experience, how one might approach these different tasks both before and after finding a tenure-track position, and how one might cope with the stresses these tasks induce. I will also compare and contrast how these key aspects play a role in pursuing such a position in Europe as opposed to one in the USA.

Name: Kristen Barnard, Berea College (in-person)

Title: Working In Reverse: Insights Gained from Being in Academia Before My PhD

Abstract: My path through graduate school at UK was certainly not the traditional path.  While I wouldn’t recommend it to anyone, I wouldn’t change a thing, and I have had opportunities that not many people could say they have had in just five years after earning their PhD.  During my sixteen years at Berea I have learned a lot about teaching and a lot about what it means to be a professor and community member at a small liberal arts college.  In my talk I will briefly share about my journey through graduate school while teaching full time, some highlights from what I have learned as a teacher, and some insights on what you can start doing now to get noticed, get hired, and get tenured at a liberal arts institution.  

Name: Stephen Sturgeon, Linquest Corporation (in-person)

Title: Good Enough for Goverment Work - Mathematics Across the DoD 

Abstract: From PDEs to simple regressions to massive linear programs, the US Department of Defense is the country’s largest business employing a wide range of mathematical methods. In this talk I will present a sampling of the experiences I’ve had working on these problems. PDEs play a critical role in research related to radiation exposure. Rapid analytical methods to pull meaning from the numbers at the speed of relevance is critical in a combat situation. Linear programs embedded in simulation software dominate the landscape of the analysis supporting the multi-billion-dollar defense budget. Working in industry also provides the experience with working