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 Registration, Coffee and Refreshments, 4th floor lounge 9:00-9:15 Welcoming remarks 9:15-10:15 Raphael Rouquier Higher Representation Theory 1 10:30-11:30 Raphael Rouquier Higher Representation Theory 2 11:30-2:00 Lunch 2:00-3:00 Joshua Sussan Categorical Heisenberg and related structures 3:30-4:30 You Qi Categorification of small quantum groups July 7, 2014, Monday Higher Representation Theory 3 Higher Representation Theory 4 11:15-2:00 Lunch 2:00-3:00 Alex Ellis Odd categorification of quantum sl(2) 3:30-4:30 David Rose Knots and representation theory: from the Jones polynomial to Khovanov-Rozansky homology via skew Howe duality 4:40-5:30 Discussion 1
July 8, 2014, Tuesday Higher Representation Theory 5 Higher Representation Theory 6 11:15-2:00 Lunch 2:00-3:00 Weiqiang Wang BGG Category O is a categorified Schur duality 3:30-4:30 David Hill Quantum Shuffles and Categorification 4:40-5:30 Discussion July 9, 2014, Wednesday Higher Representation Theory 7 Higher Representation Theory 8 11:30-2:00 Lunch 2:00-3:00 Yiqiang Li Geometric Schur duality of classical type 3:30-4:30 Punita Batra TBA 4:40-5:30 Discussion July 10, 2014, Thursday Higher Representation Theory 9 Higher Representation Theory 10 2
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-Reshetikhin- Turaev 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 3
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 sl 2 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 sl m 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. 4
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 5
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. 6