2024
Louis Kauffman
Louis Hirsch Kauffman has a B.S. from MIT (1966) and a PhD. from Princeton University (1972). He is Professor of Mathematics Emeritus at the University of Illinois at Chicago.His research is primarily in knot theory and its relationships with combinatorics and physics. He is known for the construction of knot products and branched vibrations in high dimensional knot theory, the discovery of state summation models for the Alexander-Conway polynomial, the Kauffman Bracket Polynomial state sum model for the Jones polynomial, the two-variable Kauffman polynomial and for the discovery of virtual knot theory, a diagrammatic theory of knots and links in thickened surfaces.Kauffman is author of four books on knot theory and many research papers. He is a Fellow of the American Mathematical Society since 2014. He received two Lester R. Ford Awards of the Mathematical Association of America (1978, 2014). He received the Warren McCulloch Memorial Award (1993) and the Norbert Wiener Medal (2014) of the American Society for Cybernetics. Kauffman is a recipient of the Bertalanffy prize (2016) for complexity thinking.
Public lecture
May 23, 4pm-5pm (lecture), 5pm-6pm (reception), Burwell Center for Career Achievement 340
Knots and Physics
Abstract: This talk will graphically illustrate surprising connections between the topology of knots and fundamental aspects of physics.
Knots are physical to begin with, being patterns of the way rope can be entangled in space. In the 19th century, Lord Kelvin (Sir William Thompson) hypothesized that atoms of matter were identical with knotted vortices in the luminiferous aether. This led to collaborations of Kelvin with mathematicians such as Peter Guthrie Tait, and the production of the first tables of knots and links. The Kelvin theory had its problems (stability of the vortices) and by the turn of the century, certainly after Einstein and his miracle year of 1905, the luminiferous aether was abandoned and so along with it the Kelvin vortex theory. Nevertheless, those vortices and the knots lived on in people’s research. Knots were studied in the newly emerging field of topology and vortices were studied in fluid dynamics. The theme of relations between knots and physics continued even without the aether. It was not until 1912 and the work of Kleckner and Irvine that knotted vortices were first seen in a real fluid (knotted vortices in water).
Yet in the 1980’s there was a breakthrough in knot theory and its relationships with statistical mechanics and quantum field theory that led to the emergence of many new invariants of knots, links and three manifolds (Jones, Kauffman, Homflypt polynomials, Witten invariants via quantum field theory, Vassiliev invariants) and by the turn of the century new homology theories (Khovanov Homology, Heegaard-Floer Knot Homology) related to these invariants emerged.
In this talk we will trace some of this history in a self-contained way, and we will tell a particular research story about how new invariants of knots and links can be used to study the degeneration and reconnection of vortices in fluids. If there is time, we will discuss speculative theories of the present day about the relationship of knots and elementary particles.
Seminar for experts
May 24, 4-5pm, Knudson 309
Coloring Trivalent Graphs, Penrose State Sums and Virtual Knot Theory
2023
Ole Warnaar
Ole Warnaar is a Professor of Mathematics at the University of Queensland. He works at the intersection of algebraic combinatorics, special functions, additive number theory and representation theory. He is best known for his work on elliptic hypergeometric series, Selberg integrals and identities of the Rogers-Ramanujan type. Prof. Warnaar is an elected fellow of the Australian Academy of Science, he received the George Szekeres medal of the Australian Mathematical Society in 2019, and he served as the President of the Australian Mathematical Society in 2020-21.
Public lecture
May 19th, 3-4pm, Olin 105
The story of the Rogers-Ramanujan identities
Abstract: The Rogers-Ramanujan identities are a pair of q-series identities that first appeared in a largely-ignored paper by L.J. Rogers in 1894. They rose to prominence in 1913 thanks to the famous correspondence between the self-taught Indian genius Srinivasa Ramanujan and G.H. Hardy in Cambridge. In this lecture I will discuss the intriguing and ongoing story of the Rogers-Ramanujan identities, from their origin in the work of Rogers, Ramanujan and Schur to more occurrences in such wide-ranging fields as knot theory, number theory, representation theory and statistical mechanics.
Seminar for experts
May 18, 4-5pm, Knudson 309
Virtual Koornwinder integrals
2020
Anne Schilling
Dr. Schilling received her PhD from SUNY Stony Brook in 1997. She was the recipient of a Humboldt Research Fellowship and Simons Fellowship. She is currently a professor at the University of California at Davis and a Fellow of the American Mathematical Society. Her research interests range from algebraic combinatorics to representation theory to mathematical physics. One focus is the theory of crystal bases and she has recently written a textbook on the topic with Daniel Bump from Stanford University. She has also used combinatorial techniques and semigroup theory to answer questions in probability.
Public lecture
November 19th, 2020, Olin 105
New ideas about Markov chains
Abstract: We will discuss some new ideas from semigroup theory to analyze the stationary distribution and mixing time of finite Markov chains. An example for a Markov chain is card shuffling and a natural question is: how often do you have to shuffle the deck before it is mixed or random? It turns out that semigroup theory can help answer these questions.
The video recording of this talk is available at https://cs.du.edu/~mathfiles/Videos/AnneSchilling.mp4
2019
George Andrews
Prof. George Andrews is a leading expert in the theory of partitions. He wrote over 250 research and popular articles on q-series, special functions, combinatorics and applications. Prof. Andrews is a member of the National Academy of Sciences, fellow of the American Academy of Arts and Sciences, and a fellow of the American Mathematical Society. He also served as the president of the American Mathematical Society.
Public Lecture
May 30, 4-5pm, Olin 105
Ramanujan's Lost Notebooks in Five Volumes --- Reflections
Abstract: Bruce Berndt and I have recently completed the fifth and final volume on Ramanujan's Lost Notebook. All of Ramanujan's assertions (with perhaps one of two exceptions) have been proved or, in very rare instances, refuted or corrected. Among these hundreds of formulas there are a number that stand out. For example, the recent explosion of results on mock theta functions and mock modular forms has it origin in the Lost Notebook. The "sums-of-tails" phenomenon also arose from the Lost Notebook. This talk will be a personal account of highlights from this project and questions, yet to be answered, that arose from this decades long effort.
2018
Vitaly Bergelson
Dr. Bergelson received his PhD from Hebrew University in 1984. He is a Distinguished Professor of Math and Physical Sciences at Ohio State University and a Fellow of the American Mathematical Society. His areas of expertise are ergodic theory, combinatorics, ergodic Ramsey theory, polynomial Szemerédi's theorem and number theory. Prof. Bergelson's well-known results include the Bergelson-Leibman theorem and a polynomial generalization of Szemerédi's theorem that provided a positive solution to the Erdős-Turán conjecture.
Public lecture
May 24, 4-5pm, Olin 105
The Many Facets of the Poincaré Recurrence Theorem
Seminar for experts
May 25, 2pm
Uniform distribution, generalized polynomials and the theory of multiple recurrence
2017
Nitu Kitchloo
Dr. Kitchloo received his PhD from MIT in 1998. He is a Professor and current Chairman of the Department of Mathematics at Johns Hopkins University, and he received the the Simons Fellowship for 2017-2018. His early work was on the topology of certain infinite dimensional groups known as Kac-Moody groups. He has since worked on various topics including Symplectic Topology, Differential Geometry, Stable Homotopy theory and Homotopical aspects of Mathematical Physics.
Public Lecture
May 18, 3-4pm, Olin 105
Abstraction, Reality and the Study of Mathematics
Seminar for experts
May 19, 2pm
The Stable Symplectic Category and a Conjecture of Kontsevich
2016
Mathai Varghese
Mathai Varghese received his Ph.D. in Mathematics from the Massachusetts Institute of Technology in 1986. He is the Sir Thomas Elder Professor of Mathematics at the University of Adelaide, Australia, and is a Fellow of the Australian Academy of Science. His research is mainly focused on Geometric Analysis and Mathematical Physics. He is internationally renowned for the Mathai-Quillen formalism in topological field theories, for his work on the Atiyah-Singer index theory and for T-duality in String Theory in a background flux.
Public lecture
May 17, 4-5pm, Olin 105
Exotic Symmetries in String Theory
Seminar for experts
May 20
Atiyah-Singer index theory, fractional variant and applications
2015
David Aldous
David Aldous received his Ph.D. from Cambridge University in 1977. He is a Professor in the Statistics Department at UC Berkeley, Fellow of the Royal Society, and a member of the National Academy of Sciences. His research in mathematical probability has covered weak convergence, exchangeability, Markov chain mixing times, continuum random trees, stochastic coalescence and spatial random networks. A central theme in the works of Dr. Aldous is the study of large finite random structures, obtaining asymptotic behavior as the size tends to infinity via consideration of some suitable infinite random structure.
Public lecture
May 28, 4-5pm, Olin Hall 105
Probability, outside the classroom
Seminar for experts
May 29, 10am, Aspen Hall 018
