Download CBMS Conference on Higher Representation Theory Schedule of

CBMS Conference on
Higher Representation Theory
Schedule of Talks
(all talks are held in SAS 1102, NCSU)
July 6, 2014, Sunday
8:30-9:00
9:00-9:15
9:15-10:15
10:30-11:30
11:30-2:00
2:00-3:00
3:00-3:30
3:30-4:30
Registration, Coffee and Refreshments, 4th floor lounge
Welcoming remarks
Raphael Rouquier
Higher Representation Theory 1
Raphael Rouquier
Higher Representation Theory 2
Lunch
Joshua Sussan
Categorical Heisenberg and related structures
Coffee Break
You Qi
Categorification of small quantum groups
July 7, 2014, Monday
8:30-9:00
9:00-10:00
10:15-11:15
11:15-2:00
2:00-3:00
3:00-3:30
3:30-4:30
4:40-5:30
Coffee and Refreshments, 4th floor lounge
Raphael Rouquier
Higher Representation Theory 3
Raphael Rouquier
Higher Representation Theory 4
Lunch
Alex Ellis
Odd categorification of quantum sl(2)
Coffee Break
David Rose
Knots and representation theory: from the Jones polynomial to Khovanov-Rozansky homology via skew Howe
duality
Discussion
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July 8, 2014, Tuesday
8:30-9:00
9:00-10:00
10:15-11:15
11:15-2:00
2:00-3:00
3:00-3:30
3:30-4:30
4:40-5:30
Coffee and Refreshments, 4th floor lounge
Raphael Rouquier
Higher Representation Theory 5
Raphael Rouquier
Higher Representation Theory 6
Lunch
Weiqiang Wang
BGG Category O is a categorified Schur duality
Coffee Break
David Hill
Quantum Shuffles and Categorification
Discussion
July 9, 2014, Wednesday
8:30-9:00
9:00-10:00
10:15-11:15
11:30-2:00
2:00-3:00
3:00-3:30
3:30-4:30
4:40-5:30
Coffee and Refreshments, 4th floor lounge
Raphael Rouquier
Higher Representation Theory 7
Raphael Rouquier
Higher Representation Theory 8
Lunch
Yiqiang Li
Geometric Schur duality of classical type
Coffee Break
Punita Batra
TBA
Discussion
July 10, 2014, Thursday
8:30-9:00
9:00-10:00
10:15-11:15
Coffee and Refreshments, 4th floor lounge
Raphael Rouquier
Higher Representation Theory 9
Raphael Rouquier
Higher Representation Theory 10
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Abstracts
Punita Patra
TBA
Alex Ellis
Odd categorification of quantum sl(2)
We categorify covering quantum sl(2) using a diagrammatic super-2-category.This
super-2-category admits a 2-representation in which it acts on cyclotomic quotients of odd nilHecke algebras. Time permitting, we will discuss a variant which
gives a categorification at a fourth root of unity.
David Hill
Quantum Shuffles and Categorification
The induction product on finite dimensional representations of quiver Hecke
algebras corresponds to a q-deformed shuffle product at the level of the associated quantum group. We extend the quantum shuffle model to quantum
supergroups of basic type. Using this model, one can describe the representation theory of the quiver Hecke superalgebras associated to osp(1|2n) defined
by Kang-Kashiwara-Tsuchioka, and the dg-algebra categorifying gl(1|n) due
to Khovanov-Sussan. Finally, our construction predicts a categorification of
osp(2|2n) as well. (Joint with S. Clark and W. Wang).
Yiqiang Li
Geometric Schur duality of classical type
Ill talk about a generalization of the classic work of Beilinson, Lusztig and
MacPherson on the geometric realization of quantum gl(n) by using partial flag
varieties. This is joint with Huachen Bao, Jonathan Kujawa and Weiqiang
Wang.
You Qi
Categorification of small quantum groups
We propose an algebraic approach to categorification of quantum groups at a
prime root of unity, in the scope of eventually categorifying Witten-ReshetikhinTuraev three-manifold invariants. This is joint work with Mikhail Khovanov.
David Rose
Knots and representation theory: from the Jones polynomial to
Khovanov-Rozansky homology via skew Howe duality
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We’ll discuss recent work on the relationship between (categorified) invariants of knots in the 3-sphere and (higher) representation theory. More specifically, we’ll show how the diagrammatic, Kauffman bracket formulation of the
Jones polynomial can be derived from the representation theory of quantum sl2
via skew Howe duality. We’ll then see how this picture categorifies, showing that
Khovanov homology can be viewed as a 2-representation of categorified quantum
slm via categorical skew Howe duality. Time permitting, we’ll also discuss how
this extends to give a completely elementary formulation of Khovanov-Rozansky
link homology in terms of certain singular surfaces called foams.
Joshua Sussan
Categorical Heisenberg and related structures
A graphical category whose Grothendieck group contains a Heisenberg algebra was constructed by Khovanov. By considering certain complexes in the
corresponding homotopy category we obtain a conjectural boson-fermion correspondence on the level of categories. We will also study a super version of
Khovanov’s category in order to obtain a twisted Heisenberg algebra.
Weiqiang Wang
BGG Category O is a categorified Schur duality
We first explain and justify the title in the setting of type A. Then we
develop a new Schur-type duality featuring Hecke algebra of type B, and use it
to initiate a new theory of canonical basis arising from quantum symmetric pairs.
This allows us to formulate and establish for the first time the KL conjecture
of the ortho-symplectic Lie superalgebras; in particular, this provides a new
reformulation of KL theory of classical Lie algebras. This is joint work with
Huanchen Bao (Virginia). We will discuss the general types and applications,
time permitting.
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Check-in Information at Guest Rooms
The Guest room complex is located in Avent Ferry Complex, see direction
below.
The main desk at Avent Ferry is staffed from 1:00pm until 9:00pm daily,
including July 4th. Guests will check in at the service desk in Avent Ferry Swan Quarter Hall (Building D) to pick up keys. We’ll plan for the majority of
arrivals on the afternoon of Saturday, July 5th.
If you have early arrivals or late arrivals on the weekend (outside of the 1pm
- 9pm time frame), please notify our Summer Conference Coordinator on duty
at 919-513-2799 so they can meet you to have your guests checked in.
Transportation Information
We have arranged airport pick-up service on July 5 and drop off on July 10.
We will have a van running periodically depending on need.
If you have not done so, please provide your flight information with arrival
time at Raleigh-Durham Airport. Your arrival will be either terminal A or C
depending on the airlines. In either case, please come to the luggage claim area
for pick-up.
If you take a taxi or are driving please note that conference housing is Guestroom at Avent Ferry Complex on Western Blvd and Avent Ferry Road Street.
If you stay in hotels, they usually provide a free airport pick-up service. You
will need to call in advance to save waiting time. Their van leaves for the airport
at every hour from 7 am to 10 pm.
If we miss you, you can take a taxi or TTA Bus No. 100 (use Downtown
direction to come to the department). The bus service is available from 7am
till 10 pm. The nearest stop is the NCSU Bell Tower located on Hillsborough
Street bordering the campus.
Registration
Please go to the Math building (SAS Hall) Sunday morning before 8:30 and
pick up your name tags and conference materials.
Driving Direction
The conference housing is Guest Rooms in Avent Ferry Complex at the intersection of Bestern Bulivard and Avent Ferry Road, approximately 10 minute
walk in the south of the campus.
In the following we include the direction to Avent Ferry Complex.
Coming From Interstate 85:
1.Take I-85 (north or south, depending on where you started) until you get
to the I-40 junction. From there, take I-40 East.
2.Continue until you get to Exit 289 - The Wade Avenue Exit. Taking this
exit will lead you into the heart of Raleigh. After exiting off I-40, continue on
Wade Avenue until you get to street (it will be the second stoplight).
3.There will be a shopping center to your left, and signs indicating Meredith
College to the right. Turn right at this stoplight onto Faircloth Street. Continue on Faircloth Street, and pass through Hillsborough Street and turn left
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to Western Bulivard. Drive on Western and turn right on Avent Ferry Road.
The Guestrooms are located in the Avent Ferry Complex at the intersection of
Avent Ferry and Western Bulivard.
Coming from I-40 Heading East:
1.Take I-40 until you get to Exit 289 - Wade Avenue Exit. Then follow (2)
and (3) above.
Coming From Interstate 95:
1.Take I-95 (north or south, depending on where you started from) until you
get to the I-40 junction. Take the I-40 West exit. From there follow the I-40
directions below...
Coming from I-40 Heading West:
1.Take I-40 into Raleigh (you’ll know you’re in Raleigh when you see the
sign ”Raleigh Next 9 Interchanges”).
2.You will then enter the beltline. Be sure to take I-40 West-Durham, be
sure you do not take I-440 North and East Raleigh. In short, do not exit off
I-40.
3.At Exit 295 - Gorman Street get off I-40. After exiting, take a right onto
Gorman Street. Then drive on Gorman until you reach Avent Ferry Road. Turn
right onto Avent Ferry Road and continue until Western Bvld. The Avent Ferry
Complex is at the intersection of Western and Avent Ferry.
Coming from Raleigh-Durham International Airport:
Leave the airport and get on Aviation Parkway (towards I-40). You can
either then take Airport Boulevard to I-40 or follow Aviation Parkway to I-40.
At the I-40 junction, take the I-40 East exit. This exit will get you on I-40
headed in the right direction.
1.Take I-40 until you get to Exit 289 - Wade Avenue Exit. Then follow (2)
and (3) from the section of “Coming From Interstate 85:”.
Parking
The conference will be held in SAS Hall in Room 1102. In order to park on
campus you will need a parking permit which can be purchased at the visiting
booth at Sullivant Drive.
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