Lectures to be held October 2nd and 3rd.
October 2, 2017
|4:00pm - 5:00pm||BESC 180||
Homotopy theory and its many roles in mathematics
This talk will be a historical summary of the origins of homotopy theory, and especially homotopy groups, and the many roles they plan in mathematical subject, ranging from the classification of manifolds to the classification of symmetry protected phases of matter.
Reception to follow Lecture at the Koenig Alumni Center, 1202 University Avenue, 5:00 - 7:30pm
October 3, 2017
|4:00pm - 5:00pm||HALE 270||
Topological quantum field theories
The notion of a topological quantum field theory was introduced by Witten in 1989 and axiomatized by Atiyah and Segal shortly after. It has turned out to be a surprisingly rich scheme. In this talk I will describe this notion, and how in certain circumstances it allows one to solve classification problems in condensed matter physics. Much of the material described in this talk represents joint work with Dan Freed.
Michael J. Hopkins
| Professor Michael J. Hopkins of Harvard University is one of the most important figures in the development of modern algebraic topology. He received his PhD from Northwestern University under the supervision of Mark Mahowald in 1984 and has been a driving force in the field since then. His work has influenced mathematics across fields.
In stable homotopy theory, his work on chromatic phenomena and topological modular forms have reshaped the subject. In manifold theory, his work with Hill and Ravenel almost completely resolves the Kervaire invariant problem, which has been open since the 1960s. The methods used in the solution of this problem have transformed algebraic topology. Recently, his influence has spread to mathematical physics with his study of twisted K-theory, TQFTs and Chern-Simons theories in various collaborations with Daniel Freed, Jacob Lurie and Constantin Teleman. In addition to his scientific achievements, Michael Hopkins played a tremendous role in educating younger mathematicians. He has supervised more than 15 graduate students, among whom are Jacob Lurie (Harvard) and Michael Hill (UCLA).
Michael Hopkins is also a phenomenal lecturer. He has received numerous awards and has been invited to give many distinguished lectures. Among others, in 2000, he gave the Marston Morse Memorial Lectures at the Institute for Advanced Study and the Namboodiri Lectures at the University of Chicago. He was a plenary speaker at the ICM in 2002. In 2012, he received the NAS Award in Mathematics from the U.S. National Academy of Sciences and in 2014, he received the Frederic Esser Nemmers Prize in Mathematics from Northwestern University.
This Lecture Series is funded by an endowment given by Professor Ira M. DeLong, who came to the University of Colorado in 1888 at the age of 33. Professor DeLong essentially became the mathematics department by teaching not only the college subjects but also the preparatory mathematics courses. Professor DeLong was a prominent citizen of the community of Boulder as well as president of the Mercantile Bank and Trust Company, organizer of the Colorado Education Association, and president of the charter convention that gave Boulder the city manager form of government in 1917. After his death in 1942 it was decided that the bequest he made to the mathematics department would accumulate interest until income became available to fund DeLong prizes for undergraduates and DeLong Lectureships to bring outstanding mathematicians to campus each year. The first DeLong Lectures were delivered in the 1962-63 academic year.