Workshop on Elliptic Curves, Torsors, and Lfunctions
March 2427, 2017University of Virginia, Charlottesville, VAOrganized by Andrew Obus, Andrei Rapinchuk and Lloyd WestSponsored by the NSF, UVa Department of Mathematics and the Institute of Mathematical ScienceThe workshop will be followed by the lectures of B. H. Gross in the distinguished lecture series Virginia Mathematics Lectures March 2729, 2017 

Speakers:  
Mirela Çiperiani  University of Texas 
Vladimir Chernousov  University of Alberta 
Pete Clark  University of Georgia 
Wei Ho  University of Michigan 
Kiran Kedlaya  University of California, San Diego 
Alexander Merkurjev  University of California, Los Angeles 
Raman Parimala  Emory University 
Gopal Prasad  University of Michigan 
Sujatha Ramdorai  University of British Columbia 
Arul Shankar  Harvard Univeristy 
Lucien Szpiro  City University of New York 
John Voight  Dartmouth College 
For further information, please contact one of the organizers or email workshop@virginia.edu
Participants
Nivedita Bhaskhar  UCLA 
Kestutis Cesnavicius  UC Berkeley 
Valdimir Chernousov  University of Alberta 
Michael Chou  University of Connecticut 
Mirela Çiperiani  University of Texas 
Pete Clark  University of Georgia 
Joseph Gunther  City University of New York 
Bastian Haase  Emory University 
Wei Ho  University of Michigan 
Kiran Kedlaya  University of California, San Diego 
Bao V. Le Hung  University of Chicago 
Brandon Levin  University of Chicago 
Eli Matzri  BarIlan University 
Alexander Merkurjev  University of California, Los Angeles 
Sumit Chandra Mishra  Emory University 
Jackson Morrow  Emory University 
Raman Parimala  Emory University 
Gopal Prasad  University of Michigan 
Sujatha Ramdorai  University of British Columbia 
Igor Rapinchuk  Michigan State University 
Arul Shankar  Harvard Univeristy 
Lucien Szpiro  City University of New York 
Sergey Tikhonov  Belarusian State University 
Ila Varma  Harvard University 
John Voight  Dartmouth College 
Titles and Abstracts
Talks
1. Are the elements of the TateShafarevich group divisible within the
WeilChatelet group? (Cassels' question)
2. How does the TateShafarevich group intersect the maximal
divisible subgroup of the WeilChatelet group? (Bashmakov's
question)
We will discuss our answers to these questions. This is joint work with Jakob Stix.
Short Communications
However it is a theorem of Merkurjev/Rost that for central simple algebras of degree 4, the Whitehead group is trivial over fields of cohomological dimension 3. This is a consequence of an injection of $\mathrm{SK}_1(A)$ into a subquotient of the degree 4 Galois cohomology group which led Suslin to ask whether the same was true for index $\ell^2$ algebras for any prime $\ell$ over cohomological dimension 3 fields. In this talk, we address this question for $\ell$torsion, degree $\ell^2$ algebras over function fields of $p$adic curves where $\ell$ is any prime not equal to $p$. The proof relies on the techniques of patching as developed by HarbaterHartmannKrashen and exploits the arithmetic of these fields to show triviality of the reduced Whitehead group.
Schedule
All talks on Friday  Sunday (3/24  3/26) will be in KER 317, and tea/coffee breaks in the lounge across the hall.
The breakfasts on Saturday and Sunday (3/25 & 3/26) will also be in the lounge.
Short communications on Monday (3/27) will be in Dell 2 100.
Friday, March 24 (please note changes!)
1:30  2:20 

2:30  3:15 
Tea 
3:15  4:05 
Saturday, March 25
9:00  9:30 
Light breakfast 
9:30  10:20 

10:30  11:20 

11:30  12:00 
Tea 
12:00  12:50 

1:00  2:45 
Lunch 
2:45  3:35 

3:45  4:15 
Tea 
4:15  5:05 

5:15  6:05 

6:30  8:30 
Dinner at Afghan Kabob (400 Emmet St.) 
Sunday, March 26
9:15  10:00 
Light breakfast 
10:00  10:50 

11:00  11:50 

12:00  12:50 

1:00  3:00 
Lunch 
Short communications
3:00  3:20  
3:30  3:50  
4:00  4:30 
Tea 
4:30  4:50  
5:00  5:20  
5:30  5:50 
Monday, March 27 (in Dell 2 100)
Short communications
9:00  9:20 

9:30  9:50 

10:00  10:20 

10:30  11:00 
Tea 
11:00  11:20 

11:30  11:50  
12:00  12:20  
 
 

Slides
Practical Tips
1. Hotel information.
The hotel is The Graudate Charlottesville (1309 West Main Street, (434) 2954333, website). It is located at the intersection of West Main Street and 13th Street NW. If you are coming from the airport, you should take a taxi or Uber and ask for a receipt (for travel reimbursement). If you are coming from the train station, it is an easy walk from there (less than half a mile). Go up the staircase opposite the station house. The street you see is West Main Street. Cross to the far side and walk left along West Main Street until you reach the hotel.
2. Wifi.
You can get a passcode to access wifi on the UVA grounds (i.e. campus) from Raven James in the math office in Kerchof Hall (see below for directions to Kerchof Hall). Please pick up your reimbursement form at the same time.
3. UVA grounds information.
The easiest way to
find your way around UVA is to use the interactive web map available
here: map (also click links below). The buildings of relevance
as far as the workshop are:
(1) Kerchof Hall  #22 on the
McCormick Road Area map  this is where the Math Department is located, and where all of the
lectures on Friday, Saturday, and Sunday will take place (official address 141
Cabell Drive);
(2) Physics  #41 on the McCormick Road Area map,
where Prof. Gross's Monday and Wednesday lectures will take place;
(3) Monroe Hall  #26 on the Central Grounds map, where
Prof. Gross's Tuesday lecture will take place;
(4) Dell 2  #52 on
the McCormick Road Area map, where Monday's short communications will
take place.
Googlemaps knows the way to Kerchof Hall (by name or as 141 Cabell Drive). Specifically, to reach Kerchof from the hotel, exit onto West Main Street, turn left, cross West Main Street at the first crosswalk, and then turn right onto Jefferson Park Avenue. Walk down Jefferson Park Avenue until you reach Brandon Avenue. At this point, cross Jefferson Park avenue and walk up the ramp to the left. Once up the ramp, continue to walk straight until you reach a staircase. When you get to the top of this staircase, you will be in a small parking lot. Walk along the parking lot as it curves to your left. Eventually, you will see Kerchof Hall on your left. The whole walk is about threequarters of a mile.
The departmental office is right across from the main entrance (this is where you need to find Raven James and get your wifi password as well as your reimbursement forms). Our offices as well as the lounge are one level above: KER 208 (Andrew), KER 229 (Lloyd), and KER 307 (Andrei). The departmental phone number is 4349244919. Another building that may be useful is Newcomb Hall  there is a food court in this building which can be used for lunch (it will be open on weekdays). The neighborhood around the hotel also has lots of restaurants for lunch and dinner.
4. Giving a Talk.
We will provide an overhead projector and a computer projector. If you wish you can connect your own laptop, but you can also copy your talk on a flash drive and use ours. You may, of course, use the chalkboard as well.
5. Dinner.
The conference dinner will be at the Afghan restaurant Afghan Kabob (400 Emmet Street N, website ), on Saturday, March 25. Despite the name, the restaurant has lots of vegetarian options. The last lecture will end at 6:05, and our dinner reservation is for 6:30, so we will leave directly from Kerchof. It is a bit under a mile from Kerchof. Some people will walk, and we will be able to offer rides for the others.
Very important: we need to tell the restaurant how many people will come, so please email Andrew (andrewobus@gmail.com) at your earliest convenience to confirm that you intend to come to dinner. The restaurant does not serve alcohol, but Andrew will lead an outing to a bar after dinner for those who would like to go out (unfortunately, we cannot reimburse alcohol).