Registration

The registration period for lodging and funding has closed (deadline was October 1, 2024).

Poster

Print the high-definition conference poster and place it around your department!

Speakers 

  (Titles and abstracts below)

• Nathan Chen (Harvard University)

• Daniel Litt (University of Toronto)

• Diane Maclagan (University of Warwick)

• Eyal Markman (University of Massachusetts at Amherst)

• Yunqing Tang (California Institute of Technology/UC Berkeley)

• Montserrat Teixidor I Bigas (Tufts University)

Schedule

BATMOBILE @ Dartmouth Fall 2024 will be held on the Friday leading up to AGNES.  Arrive early for AGNES and attend the BATMOBILE talks for a tropical bonus!  BATMOBILE talks will be held in lecture room Haldeman 041 of Haldeman Center, 29 N Main St, Hanover, NH 03755.

GEMS (Gender Equity in the Mathematical Study) of Algebraic Geometry mixer and the wine and cheese reception are open to all participants and will be held in the common room Kemeny 300, in the Mathematics Department, Kemeny Hall, 27 North Main St, Hanover, NH 03755.  Note that Haldeman Center and Kemeny Hall are two sides of the same building.

The Friday AGNES talk will be held in lecture room Kemeny 008 in Kemeny Hall.

All Saturday and Sunday AGNES talks and pre-talks will be held in Filene Auditorium in Moore Psychology Building, 3 Maynard St, Hanover, NH 03755. 

The poster session, computational algebraic geometry sessions, and the banquet will be held in the Hanover Inn, 2 East Wheelock Street, Hanover, NH 03755.

For the banquet, we request that faculty pay $40, postdocs pay $30, and graduate students pay $20 upon registration.  Payment accepted by cash or Venmo at registration.

All gender and single occupancy restrooms on campus can be found on a layer of this campus map including one located on the 3rd floor of Kemeny Hall near office 342.

Friday BATMOBILE (Haldeman 041):

• 11:00-12:00 Mario Sanchez Derived categories of permutahedral varieties through matroids

• 12:00-02:00 Lunch

• 02:00-03:00 Greg Smith Cohomology of toric vector bundles

Friday, November 8 (Kemeny 008):

• 03:00-04:30 GEMS of Algebraic Geometry mixer (Kemeny 300)

• 04:30-06:00 Diane Maclagan Tropical vector bundles

• 06:00-07:00 Wine and cheese reception (Kemeny 300)

Saturday, November 9 (Filene Auditorium and Hanover Inn):

• 08:30-09:00 Coffee and donuts

• 09:00-09:25 Pre-talk (Eyal Markman)

• 09:30-10:30 Eyal Markman Cycles on abelian 2n-folds of Weil type from secant sheaves on abelian n-folds

• 10:30-11:00 Break

• 11:00-12:00 5-minute research talks (parallel sessions in Moore Hall 110, 150, B03) 

• 12:00-01:30 Lunch Break (catered outside Filene Auditorium)

• 01:30-01:55 Pre-talk (Yunqing Tang)

• 02:00-03:00 Yunqing Tang The arithmetic of power series and applications to periods

• 03:00-03:30 Break 

• 03:30-03:55 Pre-talk (Daniel Litt)

• 04:00-05:00 Daniel Litt On the converse to Eisenstein's last theorem

• 05:00-06:30 Break (and poster set-up)

• 05:15-06:15 Computational algebraic geometry problem session (Hanover Inn Ford Sayre Room)

• 06:30-08:00 Poster session (Hanover Inn Grand Foyer)

• 08:00-09:30 Conference dinner (Hanover Inn Grand Ballroom)

Sunday (Filene Auditorium):

• 08:30-09:00 Coffee and donuts 

• 09:00-10:00 Nathan Chen Curves on complete intersections and measures of irrationality

• 10:00-10:30 Break

• 10:30-10:55 Pre-talk (Montserrat Teixidor i Bigas)

• 11:00-12:00 Montserrat Teixidor i Bigas Brill-Noether loci, theta-characteristics, and reducible Hilbert schemes

Abstracts

• 5-minute research talk abstracts

• Poster session abstracts

• Nathan Chen Curves on complete intersections and measures of irrationality

Abstract: Given a projective variety X, one can ask if there exist curves on X that have smaller numerical invariants than those coming from slicing by some ample divisors. For a general complete intersection X of large degrees, we show that there are no curves on X of smaller degree, nor are there curves of asymptotically smaller gonality. This verifies a folklore conjecture on the degrees of subvarieties of complete intersections as well as a conjecture of Bastianelli-De Poi-Ein-Lazarsfeld-Ullery. Joint work with Ben Church and Junyan Zhao.

• Daniel Litt On the converse to Eisenstein's last theorem

Abstract: In 1875, Lazarus Fuchs asked how to recognize when an ordinary differential equation has a solution which is an algebraic function. For linear ODE, there is a now-standard conjectural arithmetic answer to this question: the Grothendieck-Katz p-curvature conjecture. I will report on joint work with Josh Lam in which we study a variant of this conjecture suitable for application to non-linear ODE, closely tied to a theorem proved by Eisenstein in 1852, the year he died of tuberculosis at the age of 29. I'll explain how to prove this conjecture for many ODE--both linear and non-linear--at initial conditions "of algebro-geometric origin."

• Diane Maclagan Tropical vector bundles

Abstract: Tropicalization replaces a variety by a combinatorial shadow that preserves some of its invariants.  When the variety is a subspace of projective space the tropical variety is determined by a (valuated) matroid.  I will review this, and discuss a resulting definition for a tropical vector bundle in the context of tropical scheme theory.  This is joint work with Bivas Khan.

• Eyal Markman Cycles on abelian 2n-folds of Weil type from secant sheaves on abelian n-folds

Abstract: Let X be an n-dimensional abelian variety and let A be the 2n-dimensional abelian variety A=X x Pic0(X). Automorphisms of the cohomology of X induced by autoequivalences of the derived category of X and by monodromy operators are both elements of the derived monodromy group DMon(X)=Spin(2n,2n). The cohomology ring H(X) is the spin representation of DMon(X), the even and odd cohomologies are the half spin representations. The vector space V=H1(A) is the vector representation of DMon(X) and it comes with a symmetric bilinear pairing. The Grassmannian IGr+ of even maximal isotropic subspaces of V naturally embeds in the projectivization of the half-spin representation Hev(X). A coherent sheaf E on X is a K-secant sheaf, if its Chern character ch(E) belongs to a line secant to IGr+ intersecting it in two complex conjugate points, each defined over the imaginary quadratic number field K. 

Orlov defined an equivalence F:Db(X x X) -> Db(A), which conjugates the diagonal action of DMon(X) on the tensor square H(X x X) of the spin representation to the natural action of DMon(X) on the exterior algebra H(A) of the vector representation. We show that two K-secant sheaves E' and E'' on X, with linearly independent ch(E') and ch(E'') in the same K-secant, determine a complex multiplication e:K -> EndQ(A) on A by K. Furthermore, F maps the outer tensor product of E' and the dual of E" to an object E on A, whose characteristic class ch(E)exp[-c1(E)/rk(E)] remains of Hodge type, under all deformations of the pair (A,e). The complex multiplication e determines a 2-dimensional subspace of Hodge classes in the middle cohomology of A known as Weil classes. When X is the Jacobian of a genus 3 curve, we show that there is a choice of K-secant sheaves E' and E" for which E deforms with (A,e) as a twisted sheaf in an open subset of the 9-dimensional moduli space of abelian sixfolds of Weil-type. We conclude the algebraicity of the Hodge Weil classes for all abelian sixfolds of Weil type of discriminant -1, for all imaginary quadratic number fields K.

• Yunqing Tang The arithmetic of power series and applications to periods

Abstract: Borel and Dwork gave conditions on when a nice power series with rational number coefficients comes from a rational function in terms of meromorphic convergence radii at all places. Such a criterion was used in Dwork’s proof of the rationality of zeta functions of varieties over finite fields. Later, the work of André, Bost, Charles and many others generalized the rationality criterion of Dwork in general framework of Arakelov theory and deduced many applications in the arithmetic of differential equations and elliptic curves. In this talk, we will discuss some further refinements and generalizations of the criteria of André, Bost, and Charles and their applications to modular forms and irrationality of certain periods. This is joint work with Frank Calegari and Vesselin Dimitrov.

• Montserrat Teixidor I Bigas Brill-Noether loci, theta-characteristics, and reducible Hilbert schemes

Abstract: If C is a generic curve of genus g, then the set of linear series on C of degree d and dimension r is non-empty precisely when the Brill-Noether number ρ is non-negative. The sets of curves having  linear series with negative ρ are called Brill-Noether loci. In particular, when ρ=-1, one obtains some divisors in M_g that have played a big role in our understanding of the geometry of the moduli space of curves. We will discuss how to construct Brilll-Noether loci of much higher codimension and  apply the result to the construction of curves with theta characteristics. This will provide examples of reducible Hilbert schemes of curves in projective space.

Lodging and Transportation

All participants who are provided with lodging will be staying at one of two hotels:

Hanover Inn

2 E Wheelock Street

Hanover, NH 03755

(603) 643-4300

Residence Inn Hanover/Lebanon
32 Centerra Pkwy
Lebanon, NH 03766
(603) 643-4511 

The Hanover Inn is an easily accessible 5-10 minute walk to all AGNES activities.  The Residence Inn is a 10 minute drive to all AGNES activities.  Public transit to/from the Residence Inn is limited: on Friday, the Advance Transit blue line stop at Colburn Hill is a 15 minute walk from the Residence Inn (last bus departing campus is 8:14 pm); on Friday, Saturday and Sunday, the campus connector shuttle (runs every 30 minutes) from Summit on Juniper, a 15 minute walk from the Residence Inn.  However, we are endeavoring to house many participants who have cars at the Residence Inn so they can give rides to others!

Important: There are extremely limited taxi and ride sharing services near Dartmouth.  Do not count on being able to use Uber or Lyft!  Dartmouth's travel website lists a few car service companies that you might be able to reserve in advance.

The Dartmouth Coach offers very convenient bus service between Boston South Station and Boston Logan Airport, as well as New York City, right to the center of campus.  The most convenient airports are Boston Logan (BOS, 3 hour bus ride), Manchester-Boston Regional Airport (MHT, 1.5 hour drive), Burlington Vermont (BTV, 1.75 hour drive), and (for the adventurous) Lebanon (N.H.) Municipal Airport (LEB, 10 minute drive).  Theoretically, the Amtrak "Vermonter" train runs once per day from Washington D.C. (stopping in Baltimore, Philadelphia, and New York) to White River Junction, VT (10 minutes drive from campus, or public transit on Friday using the Advance Transit green or orange line), but due to frequent track maintenance, this service may be interrupted.

Parking

Dartmouth has a wide variety of visitor parking options.  For participants staying at the Hanover Inn, valet parking is covered.  For participants staying at the Residence Inn, parking is free and easily accessible.  For participants arriving for the day, until 5 pm on Friday there are payed visitor parking spots (requiring the ParkMobile app) in select parking lots (see this map), with the closest to the talks being the Maynard Lot.  There is also street parking along North Main Street and Maynard Street, some using ParkMobile and some using credit card kiosks.  All Dartmouth parking lots are free and open to the public after 5 pm and during weekends, so for example, participants arriving for only Saturday should park (for free) in the Maynard Lot.

Organizers

Asher Auel, Juliette Bruce, Sarah Frei, Andrew Hanlon, Tristan Phillips, Salim Tayou

Funding

We gratefully acknowledge the support of the National Science Foundation, Dartmouth College's Faculty of Arts and Sciences, Dartmouth College's Guarini School of Graduate and Advanced Studies, Dartmouth College's Neukom Institute for Computational Science, Dartmouth College's Department of Mathematics, and the other host institutions of the AGNES consortium for making this event possible.