Type: Seminar

Modified: Mon 18 May 2015 1110; Tue 19 May 2015 1019; Mon 25 May 2015 0948; Thu 4 Jun 2015 1004

Distribution: World

Expiry: 24 Jun 2015

CalTitle1: CANCELLED THIS WEEK: Special Lecture Series: Webster -- Representation theory through the lens of categorical actions

Calendar2: 29 May 2015 1200-1300

CalLoc2: Carslaw 375

CalTitle2: CANCELLED THIS WEEK: Special Lecture Series: Webster -- Representation theory through the lens of categorical actions

Calendar3: 3 Jun 2015 1600-1730

CalLoc3: AGR Carslaw 829

Calendar4: 10 Jun 2015 1600-1730

CalLoc4: AGR Carslaw 829

Calendar5: 17 Jun 2015 1600-1730

CalLoc5: AGR Carslaw 829

Calendar6: 24 Jun 2015 1600-1730

CalLoc6: AGR Carslaw 829

Auth: anthonyh@como.maths.usyd.edu.au

UPDATE (June 4): Slides and hopefully also recordings of Ben Webster’s lectures are being posted here: http://www.maths.usyd.edu.au/u/AlgebraSeminar/15abstracts/webster15.html --------------------------------------------------------------------- UPDATE (May 25): Ben Webster’s visit will now start on June 1, so his scheduled talk on May 29 will be cancelled. His series will now consist just of the four talks on Wednesday afternoons at 4pm in June. Some talks may now extend beyond one hour, so I have updated the calendar entries to show a nominal finishing time of 5.30pm. ---------------------------------------------------------------------- UPDATE (May 18): Ben Webster has had to delay his arrival in Sydney for family reasons, so some postponement/recheduling of his talks will be necessary. His first scheduled talk on May 22 will definitely not take place then, and May 29 is doubtful at this stage. A revised schedule will be posted when we know his new dates. ---------------------------------------------------------------------- Ben Webster (University of Virginia) will be visiting the School from May 18 to June 26, funded by the University of Sydney International Research Collaboration Award scheme. As part of his visit he will be giving a series of 6 lectures on representation theory. The first two will take place in the usual Friday Algebra Seminar time-slot, and will be accessible to a broad algebraically-oriented audience. The subsequent lectures will be on Wednesday afternoons in the Access Grid Room. If you can attend any or all of this series, please take advantage of this extended visit by a major young American mathematician. Anthony Henderson ------------------------------------------------------------------------ Speaker: Ben Webster (University of Virginia) Web-page: http://people.virginia.edu/~btw4e/ Lecture times: 1) Friday May 22, 12-1pm, Carslaw 375 (Algebra Seminar) ***CANCELLED*** 2) Friday May 29, 12-1pm, Carslaw 375 (Algebra Seminar) ***CANCELLED*** 3) Wednesday June 3, 4-5.30pm, Carslaw 829 (Access Grid Room) 4) Wednesday June 10, 4-5.30pm, Carslaw 829 (Access Grid Room) 5) Wednesday June 17, 4-5.30pm, Carslaw 829 (Access Grid Room) 6) Wednesday June 24, 4-5.30pm, Carslaw 829 (Access Grid Room) Title: Representation theory through the lens of categorical actions Abstract: Representation theorists (and other mathematicians) have come to appreciate that a vector space or set having self-maps that satisfy certain relations can tell one a great deal about the object being studied. These talks will be about the categorified version of this principle: that a category is much easier to study when it carries an action of functors which satisfy certain relations (where, of course, one must be more careful about what relations means). In a remarkable self-similarity, many categories that are of great interest to representation theorists are themselves representations of a more complicated type. Specifically, they are special cases of a more general notion of an "action of a Lie algebra on a category." Thus, the entire representation category of all symmetric groups over a finite field is actually a representation of an affine Lie algebra. This is a very powerful notion, which both leads us to unexpected structures (such as gradings on algebras without an obvious homogeneous presentation) and to a new perspective on older results (for example, the identification of decomposition numbers with Kazhdan-Lusztig polynomials). I’ll start by discussing the case of the symmetric group and general linear groups over a finite field, and expand outward to less familiar objects like categories O for Lie algebras and Cherednik algebras. In further lectures, I’ll discuss other applications of these ideas to areas like canonical bases, algebraic geometry and knot homology.