Brown 2018




The Fall 2018
 workshop will take place at Brown University, September 21-23, 2018. 
Support is provided by NSF and Brown University.

Conference Administrator: Lori Nascimento (Brown University)

Funding provided by the National Science Foundation and Brown University.


Women@AGNES Organizers: Melody Chan, Man Wai Cheung, Rohini Ramadas

                                                                   


Speakers: 

Yaim Cooper (IAS)
Eric Larson (Stanford University)
Johannes Nicaise (University College London/KU Leuven)
Jose Rodriguez (University of Chicago)
Bernd Sturmfels (Max Planck Institute)
Brooke Ullery (Harvard University)
Anthony Várilly-Alvarado (Rice University)
Lauren Williams (Harvard University)

Schedule:

The conference talks will be held in MacMillan Hall, 167 Thayer Street, Providence, RI 02906

WOMEN@AGNES SCHEDULE
FRIDAY - 9/21/2018
 
12:00pm - 2:00pmWomen@AGNES Networking Lunch
Open to participants registered for this event
 Sharpe Refectory - Dining Room 8/9
144 Thayer Street (Rear)
2:15pm-2:45pmWomen@AGNES - Laure Flapan
Open to graduate students and postdocs of all genders
 “The Hodge Conjecture and Abelian Varieties”

The Hodge Conjecture describes a powerful dictionary between the “algebraic geometry” of a complex algebraic variety, meaning its subvarieties, and the “topology” of the algebraic variety, meaning certain of its deRham cohomology classes. Unfortunately there are relatively few cases where the Hodge Conjecture is known to be true. In particular, abelian varieties are a case where the Hodge Conjecture should be comparatively “easy” to check and so it is particularly disconcerting that there is no proof in this case. In this talk, we will introduce and motivate the Hodge Conjecture and then discuss the particular case of abelian varieties.
Barus & Holley 190
184 Hope Street
 
 3:00pm-3:30pm
 Women@AGNES - Ana Balibanu
Open to graduate students and postdocs of all genders
 "The wonderful compactification"

A complex semisimple algebraic group of adjoint type has a canonical smooth compactification that measures its behavior “at infinity.” This compactification was first introduced by DeConcini and Procesi in the 1980s, and more recently it has come to play an important role in geometric representation theory. In this talk I will explain a construction of the wonderful compactification and I will discuss some of its remarkable properties.
 Barus & Holley 190
184 Hope Street

AGNES SCHEDULE
FRIDAY - 9/21/2018
 TITLES/ABSTRACTSLOCATION
3:30pm - 4:15pmRegistration/Refreshments MacMillan Lobby (outside Room 117)
4:15pm - 5:15pmLauren Williams “Newton Okounkov bodies for Grassmannians”


In joint work with Konstanze Rietsch, we use the X-cluster structure on the Grassmannian and the combinatorics of planar bicolored graphs to associate a Newton-Okounkov body to each X-cluster. This gives, for each X-cluster, a toric degeneration of the Grassmannian. We also describe the Newton-Okounkov bodies explicitly using mirror symmetry: we show that they are polytopes whose facets can be read off from A-cluster expansions of the superpotential of Marsh-Rietsch. And we give a combinatorial formula for the lattice points of the Newton-Okounkov bodies, which has a surprising interpretation in terms of quantum Schubert calculus.  If time permits, we will discuss generalizations of some of these results to Schubert varieties.

MacMillan 117
5:30pm - 6:00pmPretalk MacMillan 117
6:00pm - 7:00pmBernd Sturmfels “Varieties of Signature Tensors”

 

The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is here examined through the lens of algebraic geometry. We introduce varieties of signature tensors for piecewise linear paths and on polynomial paths. These all live in unversal varieties that are derived from free Lie algebras and their Lie groups. This is joint work with Carlos Amendola and Peter Friz.

MacMillan 117


 
SATURDAY - 9/22/2018
 
8:30am - 9:30amRegistration/Breakfast Refreshments MacMillan Lobby (outside Room 117)
9:30am - 10:30amBrooke Ullery Measures of irrationality for algebraic varieties”

 

The gonality of a smooth projective curve is the smallest degree of a map from the curve to the projective line. There are a few different definitions that attempt to generalize the notion of gonality to higher dimensional varieties. The intuition is that the higher these numbers, the further the variety is from being rational. We will discuss these measures of irrationality and various methods of calculating and bounding them. We’ll mainly focus on the examples of hypersurfaces and, more generally, complete intersections in projective space. 

MacMillan 117
10:30am - 11:00amCoffee Break MacMillan Lobby
11:00am - 11:30amPretalk MacMillan 117
11:30am - 12:30pmJohannes Nicaise “Specialization of (stable) rationality in families with mild singularities”

 

I will present joint work with Evgeny Shinder, where we use Denef and Loeser’s motivic nearby fiber and a theorem by Larsen and Lunts to prove that stable rationality specializes in families with mild singularities. I will also discuss an improvement of our results by Kontsevich and Tschinkel, who defined a birational version of the motivic nearby fiber to prove specialization of rationality.

MacMillan 117
12:30pm - 2:30pmLunch Break 
2:30pm - 3:30pmYaim Cooper "Severi degrees via representation theory"

The Severi degrees of P1 x P1 can be computed in terms of an explicit operator on the Fock space F[P1].  We will discuss this and variations on this theme.  We will explain how to use this approach to compute the relative Gromov-Witten theory of other surfaces, such as Hirzebruch surfaces and E x P1.  We will also discuss operators for calculating descendants.  Joint with R. Pandharipande.
MacMillan 117
3:30pm - 4:00pmCoffee Break MacMillan Lobby
4:00pm - 5:00pmJose Rodriguez “Numerical computation of Galois groups and braid groups”

 

Galois groups are an important part of number theory and algebraic geometry. To a parameterized system of polynomial equations one can associate a Galois group whenever the system has k (finitely many) nonsingular solutions generically. This Galois group is a subgroup of the symmetric group on k symbols. Using random monodromy loops it has already been shown how to compute Galois groups that are the full symmetric group. In the first part of this talk, we show how to compute Galois groups that are proper subgroups of the full symmetric group. We give examples from formation shape control and algebraic statistics. In the second part, we discuss the generalization to braid groups. Braid groups were first introduced by Emil Artin in 1925 as a generalization of the symmetric group and have more refined information than the Galois group. We develop algorithms to compute a set of generators for these groups using homotopy continuation. This is joint work with Jonathan Hauenstein and Frank Sottile and with Botong Wang.

MacMillan 117
5:00pm - 7:00pmPoster Session/Reception MacMillan Lobby


 
SUNDAY - 9/23/2018
 
9:00am - 9:30amRegistration/Breakfast Refreshments MacMillan Lobby (outside Room 117)
9:30am - 10:30amEric Larson The Maximal Rank Conjecture.”

 

Curves in projective space can be described in eitherparametric or Cartesian equations. We begin by describing the MaximalRank Conjecture, formulated originally by Severi in 1915, whichprescribes a relationship between the "shape" of the parametric andCartesian equations --- that is, which gives the Hilbert function of ageneral curve of genus g, embedded in P^r via a general linear seriesof degree d. We then explain how recent results on the interpolationproblem can be used to prove this conjecture.

MacMillan 117
10:30am - 11:00amCoffee Break MacMillan Lobby
11:00am - 11:30amPretalk MacMillan 117
11:30am - 12:30pmAnthony Varilly-Alvarado "Cubic fourfolds and rational points on general K3 surfaces"

K3 surfaces are 2-dimensional analogues of elliptic curves, but without a group structure.  They don't necessarily have rational points.  However, in 2009 Skorobogatov conjectured that the Brauer group should account for all failures of local-to-global principles on K3 surfaces.  The purpose of this talk is to explain the geometric origin of certain 3-torsion classes of the Brauer group of a K3 surface, and to exploit this geometric description to show that these classes can obstruct the existence of rational points.  Fibrations of cubic fourfolds by del Pezzo surfaces of degree 6 play a key role in our work, and this project fits into framework that describes level structures of small level on low-degree K3 surfaces. This is joint work with Jennifer Berg.
MacMillan 117



PLANNING YOUR VISIT

Please use this helpful AGNES Map to navigate during the Conference.

Hotel Information:  
Rooms will be provided upon request via the AGNES Registration Form.

Hotel Rates:  Hampton $179/Night and Hilton $169/night    


Parking:

Since the conference is on the weekend, there should be plenty of on-street parking.  While most on-street parking is 2-3 hour parking, there are some streets with all day parking.  

 

There is also visitor parking in Lot 68, also called the Power Street Parking Garage (111 Power Street). Entrance to the garage is located at the intersection of Power and Thayer streets.  The lot contains two Pay and Display parking pay stations. One is located at the Power Street entrance and the second is in the far corner of the lot by Brook Street. The Pay Stations accept credit cards (Visa, MasterCard, American Express, and Discover) and U.S. bills.  The cost is $2/hour or $15/day.  Make sure to place your receipt permit visibly on your vehicle dashboard. 



Transportation:

PLEASE NOTE THAT BROWN WILL ONLY REIMBURSE COACH SEATING.

Kennedy Plaza is located just downtown. Click here for a map showing the conference site and hotels.  
Most inter-city bus lines stop here (Peter PanMegabus) as well as the airport bus
An exception is Go Busses, which stop at a different downtown location but also on college hill.
RIPTA City Buses: click here for a list of buses that travel from the station and up to the east side of Providence (where the conference will be held) and back. Click here for bus fare information. 

Providence Train Station - Click here to view the MBTA schedule, and here for Amtrak.

Air travel -  The T. F. Green airport serves many major locations. Alternatively, one can arrive at Boston's Logan airport and take bus or train to Providence. 
***PLEASE NOTE THAT WE CAN ONLY REIMBURSE FLIGHTS ON A US CARRIER, OR COUNTRIES LISTED IN THE OPEN SKIES AGREEMENT***

Reimbursement requests:

Please note that funding is limited.   We encourage graduate students and postdocs to share hotel rooms and carpool.  We will try to cover travel costs for everyone (excluding air fares), with preference given to junior participants.  


STEP 1.  Please fill out the Supplier and Individual Payee Registration Form.  Without this, I will not be able to process your reimbursement request.

STEP 2. Email a scanned copy of your original receipts to Lori@math.brown.edu.  Please make sure all receipts show proof of payment.

***Please read the instructions below if you are a foreign national:

Due to IRS/Homeland Security requirements, Brown University now requires us to verify that foreign nationals have the appropriate visa to allow for travel reimbursement.  Please note that due to Brown University's policies, we CANNOT reimburse anyone who traveled to the conference on a Tourist Visa (B-2 or VWT stamps).

We will need a copy of the following documents along with your receipts:

-Passport photo page
-Visa photo page
-Visa stamp (B-1, F-1, J-1, VWB, H-1B only)
-Most recent I-94
-Letter from institution (if on a J-1 or F-1)
-ESTA (if on a Business Waiver)
-Employment Authorization Card (if on OPT)

If you are already in the US and have a J-1 or F-1 visa, please note that you will need to obtain a letter from your home institution/department stating you are eligible for reimbursmenet before we can process your request. 

Otherwise, it is required that you obtain a B-1 visa stamp or that you have a visa Business Waiver.  In order to travel on the Visa Waiver Program, you will need to have authorization through the Electronic System for Travel Authorization (ESTA).

To see if your country is on the Visa Waiver Program list please go to this website:  https://travel.state.gov/content/travel/en/us-visas/tourism-visit/visa-waiver-program.html

Please contact the Conference Administrator, Lori Nascimento, if you have any questions.



About AGNES: AGNES is a series of weekend workshops in algebraic geometry. One of our goals is to introduce graduate students to a broad spectrum of current research in algebraic geometry. AGNES is held twice a year at participating universities in the Northeast.

Organizing committee: Dan Abramovich (Brown), Melody Chan (Brown), Brendan Hassett (Brown), Anton Leykin (Georgia Tech), Rohini Ramadas (Brown)

Steering Committee:  Melody Chan (Brown), Lev Borisov (Rutgers), Maksym Fedorchuk (Boston College), Antonella Grassi (Penn), Paul Hacking (UMass), Alina Marian (Northeastern), Sam Payne (Yale), and Christian Schnell (Stony Brook)