Herbert Howe Lecture Series

The Herbert Howe Lecture Series brings prominent mathematicians and astronomers to DU to promote current research in mathematics and astronomy. The series is named in honor of Herbert Alonzo Howe, a 19th century professor of mathematics and astronomy at the University of Denver and Denver's first astronomer.

This series is jointly hosted by the Department of Mathematics and the Department of Physics and Astronomy in the College of Natural Sciences.

Announcing the 2024 Herbert Howe Lecture

The Department of Mathematics is happy to announce that the 2024 Howe Lecture and research seminar talk will be presented by

Prof. Louis Kauffman (University of Illinois at Chicago)

About the speaker: 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 and reception

Thursday May 23, 4pm-5pm (lecture), 5pm-6pm (reception)
Burwell Center for Career Achievement, Room 340

Knots and Physics

RSVP here

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.


Research seminar

Friday May 24, time and location TBA

Coloring Trivalent Graphs, Penrose State Sums and Virtual Knot Theory


Abstract: We begin by discussing the Penrose method for counting the number of three colorings of a trivalent graph (with three distinct colors at a vertex). We show how to generalize the Penrose state summation to handle non-planar graphs and we generalize the notion of coloring to n-colorings of perfect matching graphs associated with a trivalent graph. We then show how these structures can be rewritten in terms of link diagrams and how there are significant generalizations of the Kauffman bracket polynomial associated with these Penrose generalizations. These ideas lead to the formulation of a multiple virtual knot theory and to other invariants in that theory (of quandle type) and to many questions and examples that we shall discuss. The talk will be self-contained.

Past Speakers

  • Lectures in Mathematics



    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




    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




    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.




    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





    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





    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





    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

  • Lectures in Physics


    Harold Levinson 

    Public lecture 
    Oct 11, 4-5pm, Olin 105
    The Formation of Planets from the Direct Accretion of Pebbles & the Lucy Mission to the Trojan Asteroid

    Dr. Harold (Hal) Levison received his PhD from University of Michigan in 1986 and presently is Institute Scientist at the Southwest Research Institute in Boulder. His principal research interests include the dynamics of astronomical objects. He is perhaps best known, however, for his work on the early dynamical evolution of the outer Solar System, and is an author of the most comprehensive model to date. Recently, his LUCY proposal was accepted by NASA for a spacecraft visit to the Jupiter Trojan asteroids.



    Paul Hemenway 

    Public lecture 
    Jan 25, 4-5pm, Olin 105
    Gaia - The Structure and Dynamics of the Milky Way From the Brightest Billion Stars

    Paul Hemenway started his astronomical career measuring star positions at the US Naval Observatory. He received his Ph.D. in Astronomy at the University of Virginia in 1974 measuring the positions of radio sources using Very Long Baseline Interferometry. In 1978 he became a founding member of the Hubble Space Telescope (HST) Astrometry Science Team, and used the HST Fine Guidance Sensors to help determine the coordinate system for the HIPPARCOS Astrometry Satellite. Now retired, he contributes to the Physics and Astronomy Department and the Enrichment Program at DU.



    Robert Stencel 

    Public lecture 
    September 30, 4-5pm, Olin Hall 105 
    The life, times and legacy of DU's Prof. Herbert Alonso Howe (1858-1926)

    Robert Stencel received his Ph.D. from University of Michigan in 1977. He is the William Herschel Womble Professor of Astronomy at the University of Denver, director of the DU Observatories (Chamberlin and Mt. Evans), and Colorado coordinator for the International Dark-sky Association.

    Prior to joining University of Denver in 1993, Dr. Stencel worked at NASA Houston and Greenbelt sites and at NASA Headquarters in Washington DC. He teaches astronomy courses and publishes research in astrophysics.


Herbert Howe joined the faculty in 1881 and received his doctorate in May 1884 with a thesis on a novel solution to Kepler's two body problem. He became the first director of the Chamberlin Observatory, a position in which he remained until his death in 1926.

Among his many accomplishments, he is responsible for determining the location of the original Mile High marker at the staircase of the Colorado capitol building in 1909, later replaced with an etched inscription. His measurements were more precise than those of a 1969 survey and only about 3 feet above the modern 2003 plaque.

Herbert Howe and the Chamberlin Observatory