This file can be used to add scheduled events to your calendar, however every program is unique. Below you will find what information is available, but if nothing else works try creating a new calendar in your program and using
http://math.colorado.edu/seminars/ics/topo.ics
as the source.
Thunderbird
This is the departmental seminar on algebraic topology and related topics.
We usually have a semester theme, for which speakers from the department are invited to contribute talks, and external guest speakers who will give talks on current research in topology. The semester themes for Fall 2022 are "sheaves and logic" and "applied topology". The seminar website is here.
Hours and Venue: Tuesdays, 3:30pm - 4:30pm in MATH 350
Recently, higher categorical generalizations of semiadditivity have proven useful in stable homotopy theory; in particular, they demonstrate that certain localizations of the category of spectra are exceedingly well-behaved. Understanding higher semiadditivity has also produced an interesting theory of ambidextrous adjunctions, that may be useful in the study of other stable infinity categories. In this talk, we will introduce semiadditivity and ambidexterity in a general categorical setting. We will then specialize to the context of stable homotopy theory and discuss how the theory of higher semiaddtivity gives a proof of May's nilpotence conjecture.
Ambidexterity and Nilpotence
Tue, Oct. 28 3:30pm (MATH 3…
Alex LaJeunesse
X
Machinery from homotopy theory allows us to define a Brauer space for any E_3-ring R whose homotopy groups carry important arithmetic information about R. If R is equivalent to a discrete commutative ring, for example, these homotopy groups agree with the classical (derived) unit, Picard, and Brauer groups. I will describe how one constructs this Brauer space and discuss the problem of "strictification" for Brauer classes.
Unit, Picard, and Brauer Groups of Ring Spectra
Tue, Nov. 4 3:30pm (MATH 3…
Ben Knudsen (Colorado State University)
X
The homology groups of the unordered configuration spaces of a graph form a finitely generated module over the polynomial ring generated by its edges; in particular, each Betti number is eventually equal to a polynomial in the number of particles, an analogue of classical homological stability. Wishing to lift this result to an analogue of representation stability, one encounters the unavoidable fact that the corresponding algebraic structure at the level of ordered configuration spaces is non-Noetherian. Thus, finite generation results are likely to be neither useful nor within easy reach. Drawing on ideas from twisted algebra and factorization homology, we circumvent this obstacle to give a complete asymptotic calculation of the Betti numbers of pure graph braid groups over any field and, in characteristic zero, of the multiplicities of many irreducible representations of the symmetric groups. This talk represents joint work with Hainaut and Wawrykow, building on joint work with An and Drummond-Cole.
Representation asymptotics in the homology of pure graph braid groups
Ambidexterity and Nilpotence