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Upcoming Colloquia & Seminars

  1. Joint HC & QS Colloquium: Algebraic K-theory and trace methods

    Location: MSRI: Simons Auditorium
    Speakers: Teena Gerhardt (Michigan State University)

    Algebraic K-theory is an invariant of rings which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approach to studying algebraic K-theory is via trace maps, relating algebraic K-theory to (topological) Hochschild homology, and (topological) cyclic homology. In this colloquium-style talk I will give an introduction to algebraic K-theory and its applications, and talk about modern methods to compute algebraic K-theory.

    Updated on Feb 19, 2020 01:19 PM PST
  2. (∞,2)-categories: Enriched ∞-categories

    Location: MSRI: Simons Auditorium
    Speakers: Rune Haugseng (Norwegian University of Science and Technology (NTNU))

    In the first part of the talk I will begin by introducing several ∞-categorical algebraic structures arising from the simplex category, and then use these to give a definition of enriched ∞-categories. I will also discuss some basic results about these objects, and perhaps mention some alternative definitions. In the second part I will talk about bimodules between enriched ∞-categories and Hinich's work on the Yoneda lemma. I will end by briefly talking about framed double ∞-categories (AKA proarrow equipments), which should give a good setting for doing some more category theory with enriched ∞-categories (such as enriched (co)limits and Kan extensions).

    Updated on Feb 20, 2020 11:39 AM PST
  3. (∞,2)-categories: (Op)lax natural transformations of (∞,n)-categories

    Location: MSRI: Simons Auditorium
    Speakers: Claudia Scheimbauer (TU München)

    I will explain a definition of (op)lax natural transformations for (∞,n)-categories using the model of (complete) n-fold Segal spaces. The main step in the construction is to define a family of strict n-categories (more precisely, computads), which should be thought of as what one would expect to be a Gray tensor product of the walking l-fold compositions of k-morphisms. I will explain some immediate consequences of our definitions and focus on (pictures of) low-dimensional cases. The motivation for this project was to define ``twisted field theories’’, related to relative field theories, as suggested in work by Stolz-Teichner and Freed-Teleman. If requested by the audience, I will explain briefly what I mean by this. This was joint work with Theo Johnson-Freyd.

    Updated on Feb 20, 2020 11:46 AM PST
  4. (∞,2)-categories: Polynomial functors and infinity operads

    Location: MSRI: Simons Auditorium
    Speakers: David Gepner (University of Melbourne)

    We will discuss aspects of the theory of polynomials functors and infinity operads. Time permitting we will sketch some steps in an argument (joint with Haugseng and Kock) that the infinity categories of infinity operads and analytic monads are equivalent.

    Updated on Feb 20, 2020 11:47 AM PST
  5. QS - Seminar: K-theory for operator algebras, categorification and higher twists

    Location: MSRI: Simons Auditorium
    Speakers: David Evans (Cardiff University)

    This talk is  part of a programme to understand conformal field theory through K-theory, in particular twisted equivariant K-theory.

    I describe work with Andreas Aaserud on the actions of braided C*-tensor categories on operator algebras or realizing these categories as modules over an operator algebra. Freed Hopkins Teleman realized  the Verlinde ring of positive energy representations of loop groups through twisted equivariant K-theory of the section algebra of equivariant bundles of compact operators. In work with Ulrich Pennig, we prove that each exponential functor on the category of finite-dimensional complex inner product spaces and isomorphisms gives rise to an equivariant higher (ie. non-classical) twist of K-theory over G=SU(n), employing the section algebra of a locally trivial bundle with stabilised strongly self-absorbing fibres.

    Using a version of the Mayer-Vietoris spectral sequence we compute the equivariant higher twisted K-groups for arbitrary exponential functor twists over SU(2), and also over SU(3) after rationalisation.

    Updated on Feb 21, 2020 08:54 AM PST
  6. (∞,2)-categories: Adjunctions and monads in (∞,2)-categories

    Location: MSRI: Simons Auditorium
    Speakers: Rune Haugseng (Norwegian University of Science and Technology (NTNU))

    There are three useful ways to think about a monad on an ∞-category C: as an associative algebra in endofunctors of C, as a monadic right adjoint functor to C, and as a functor from the universal monad 2-category to the (∞,2)-category of ∞-categories. These notions are known to be equivalent, thanks to work of Lurie and Riehl-Verity - but only for ∞-groupoids of monads. I will explain how to upgrade this comparison to take morphisms of monads into account. One comparison involves a general equivalence between colax morphisms of adjunctions in an (∞,2)-category and commutative squares between right adjoints, which can be proved using the expected properties of the Gray tensor product, together with results of Riehl-Verity and Zaganidis. The other (which I will probably say less about) requires comparing the natural transformations between (∞,2)-categories viewed as cocartesian fibrations over the simplex category to certain colax transformations (generalizing the "icons" of Lack).

    Updated on Feb 20, 2020 11:49 AM PST
  7. HC & QS - Graduate Student Seminar: About lines and circles: the bordism category in dimension 1 & Frobenius algebras and embedded surfaces

    Location: MSRI: Baker Board Room
    Speakers: Jan Steinebrunner (University of Oxford), Dominic Weiller (Australian National University)

    Abstract for Jan Steinbrunner:

    The 1-dimensional bordism category Cob_1 is easily defined: objects are finite oriented sets and morphisms are diffeomorphism classes of 1-dimensional bordisms, in other words: lines and circles. A close relative of Cob_1 is the (infinity,1)-category Bord_1. This is a more fancy version of Cob_1 where we don't identify diffeomorphic bordisms, but rather assemble them in an appropriate moduli space. I will recall both of these categories and how they are related. Then I'll explain why essentially the only difference between the two are the rotations of the circle, and how to make this statement precise. Finally, I'll use the universal property Bord_1 enjoys because of the cobordism hypothesis to compute the classifying space of Cob_1. Afterwards we can also talk about how to do this in dimension 2, how this relates to topological cyclic homology of \Omega X, or about any other questions that come up during the talk.

    Updated on Feb 20, 2020 11:10 AM PST
  8. Joint HC & QS Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Jan 27, 2020 03:27 PM PST
  9. HC & QS - Learning Seminar

    Location: MSRI: Baker Board Room
    Created on Jan 27, 2020 04:08 PM PST
  10. HC & QS - Blob Homology

    Location: MSRI: Simons Auditorium
    Updated on Feb 10, 2020 10:40 AM PST
  11. QS - Seminar

    Location: MSRI: Simons Auditorium
    Created on Jan 28, 2020 09:21 AM PST
  12. Joint HC & QS Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Jan 27, 2020 03:27 PM PST
  13. HC & QS - Learning Seminar

    Location: MSRI: Baker Board Room
    Created on Jan 27, 2020 04:08 PM PST
  14. Joint HC & QS Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Jan 27, 2020 03:27 PM PST
  15. HC & QS - Learning Seminar

    Location: MSRI: Baker Board Room
    Created on Jan 27, 2020 04:08 PM PST
  16. HC & QS - Blob Homology

    Location: MSRI: Baker Board Room
    Updated on Feb 10, 2020 10:45 AM PST
  17. QS - Seminar

    Location: MSRI: Simons Auditorium
    Created on Jan 28, 2020 09:21 AM PST
  18. Joint HC & QS Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Jan 27, 2020 03:27 PM PST
  19. HC & QS - Learning Seminar

    Location: MSRI: Baker Board Room
    Created on Jan 27, 2020 04:08 PM PST
  20. HC & QS - Blob Homology

    Location: MSRI: Baker Board Room
    Updated on Feb 10, 2020 10:45 AM PST
  21. QS - Seminar

    Location: MSRI: Simons Auditorium
    Created on Jan 28, 2020 09:21 AM PST
  22. HC & QS - Learning Seminar

    Location: MSRI: Baker Board Room
    Created on Jan 27, 2020 04:08 PM PST
  23. HC & QS - Blob Homology

    Location: MSRI: Baker Board Room
    Updated on Feb 10, 2020 10:45 AM PST
  24. QS - Seminar

    Location: MSRI: Simons Auditorium
    Created on Jan 28, 2020 09:21 AM PST
  25. Joint HC & QS Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Jan 27, 2020 03:27 PM PST
  26. HC & QS - Learning Seminar

    Location: MSRI: Baker Board Room
    Created on Jan 27, 2020 04:08 PM PST
  27. HC Seminar:

    Location: MSRI: Baker Board Room
    Created on Jan 27, 2020 03:30 PM PST
  28. HC & QS - Blob Homology

    Location: MSRI: Baker Board Room
    Updated on Feb 10, 2020 10:46 AM PST
  29. QS - Seminar

    Location: MSRI: Simons Auditorium
    Created on Jan 28, 2020 09:21 AM PST
  30. Joint HC & QS Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Jan 27, 2020 03:27 PM PST
  31. HC & QS - Learning Seminar

    Location: MSRI: Baker Board Room
    Created on Jan 27, 2020 04:08 PM PST
  32. HC & QS - Blob Homology

    Location: MSRI: Baker Board Room
    Updated on Feb 10, 2020 10:46 AM PST
  33. QS - Seminar

    Location: MSRI: Simons Auditorium
    Created on Jan 28, 2020 09:21 AM PST
  34. Joint HC & QS Colloquium:

    Location: MSRI: Baker Board Room
    Created on Jan 27, 2020 03:27 PM PST
  35. HC & QS - Learning Seminar

    Location: MSRI: Baker Board Room
    Created on Jan 27, 2020 04:08 PM PST
  36. HC & QS - Blob Homology

    Location: MSRI: Baker Board Room
    Updated on Feb 10, 2020 10:46 AM PST
  37. QS - Seminar

    Location: MSRI: Baker Board Room
    Created on Jan 28, 2020 09:24 AM PST
  38. Joint HC & QS Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Jan 27, 2020 03:27 PM PST
  39. HC & QS - Learning Seminar

    Location: MSRI: Baker Board Room
    Created on Jan 27, 2020 04:08 PM PST
  40. HC & QS - Blob Homology

    Location: MSRI: Baker Board Room
    Updated on Feb 10, 2020 10:46 AM PST
  41. QS - Seminar

    Location: MSRI: Simons Auditorium
    Created on Jan 28, 2020 09:21 AM PST
  42. Joint HC & QS Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Jan 27, 2020 03:27 PM PST
  43. HC & QS - Learning Seminar

    Location: MSRI: Baker Board Room
    Created on Jan 27, 2020 04:08 PM PST
  44. HC & QS - Blob Homology

    Location: MSRI: Baker Board Room
    Updated on Feb 10, 2020 10:46 AM PST
  45. QS - Seminar

    Location: MSRI: Simons Auditorium
    Created on Jan 28, 2020 09:21 AM PST
  46. HC & QS - Learning Seminar

    Location: MSRI: Baker Board Room
    Created on Jan 27, 2020 04:08 PM PST
  47. HC & QS - Blob Homology

    Location: MSRI: Baker Board Room
    Updated on Feb 10, 2020 10:46 AM PST
  48. QS - Seminar

    Location: MSRI: Simons Auditorium
    Created on Jan 28, 2020 09:21 AM PST
No upcoming events under African Diaspora Joint Mathematics Workshop