Upcoming seminars

Upcoming Seminars
Tue
02/09/2016
(today)
4:00pm
Seminar: Algebra
The Iwasawa main conjecture for elliptic curves at supersingular prime
Florian Sprung, Princeton/IAS
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W304
Iwasawa theory is a bridge between analytic objects and algebraic objects. We give a friendly introduction to the main conjecture in the ordinary case (and define what 'ordinary' means), and then outline the supersingular (=non-ordinary) theory. The main philosophy of the proof in the supersingular case is to work with a pair of simple objects similar to the ordinary ones.
Wed
02/10/2016
(tomorrow)
4:00pm
Seminar: Mathematical Physics
Finding the hidden symmetries of Nature
Maria Clara Nucci, University of Perugia
Contact: Michele Benzi, benzi@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W303
Twenty years ago David J. Gross presented, at the National Academy of Sciences, a paper entitled ``The role of symmetry in fundamental physics", which was later published in PNAS. I shall use that talk as a thread in order to illustrate my recent work related to the following main themes: (A) going from Classical to Quantum Mechanics by preserving Noether symmetries; (B) finding hidden linearity of maximally superintegrable systems; (C) determining Lagrangians (and Noether symmetries) for systems without Lagrangians. I shall provide several examples for each theme, including models in population dynamics and the Lorenz system in meteorology
Tue
02/16/2016
(in 7 days)
4:00pm
Seminar: Algebra
Hodge Theory on Matroids
Eric Katz, University of Waterloo
Contact: David Zureick-Brown, dab@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W304
The chromatic polynomial of a graph counts its proper colourings. This polynomial's coefficients were conjectured to form a unimodal sequence by Read in 1968. This conjecture was extended by Rota in his 1970 address to assert the log-concavity of the characteristic polynomial of matroids which are the common generalizations of graphs and linear subspaces. We discuss the resolution of this conjecture which is joint work with Karim Adiprasito and June Huh. The solution draws on ideas from the theory of algebraic varieties, specifically Hodge theory, showing how a question about graph theory leads to a solution involving Grothendieck's standard conjectures.
Tue
03/15/2016
(in 35 days)
4:00pm
Seminar: Algebra
Title to be announced
Jean-Louis Colliot-Thelene, Université Paris-Sud
Contact: David Zureick-Brown, dab@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W304
Fri
03/18/2016
(in 38 days)
4:00pm
Seminar: Algebra
Title to be announced
Drew Sutherland, MIT
Contact: David Zureick-Brown, dab@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W303
Thu
03/24/2016
(in 44 days)
4:00pm
Defense: Dissertation
Hasse principle for Hermitian spaces
Zhengyao Wu, Emory University
Contact: Zhengyao Wu, zwu22@emory.edu
Venue: Mathematics and Science Center, Room W302
This dissertation provides three results:\\ \\ (1) A Hasse principle for rational points of projective homogeneous spaces under unitary or special unitary groups associated to hermitian or skew hermitian spaces over function fields of $p$-adic curves;\\ \\ (2) A Springer-type theorem for isotropy of hermitian spaces over odd degree field extensions of function fields of $p$-adic curves;\\ \\ (3) Exact values of Hermitian u-invariants of quaternion or biquaternion algebras over function fields of $p$-adic curves.
Mon
03/28/2016
(in 48 days)
3:00pm
Seminar: Algebra
Thesis Defense
Mckenzie West, Emory University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room E408
Tue
03/29/2016
(in 49 days)
4:00pm
Seminar: Algebra
Thesis defense
Anastassia Etropolski, Emory University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W304
Thu
03/31/2016
(in 51 days)
4:00pm
Defense: Dissertation
R-equivalence and norm principles in algebraic groups
Nivedita Bhaskhar, Emory University
Contact: Nivedita Bhaskhar, nbhaskh@emory.edu
Venue: Mathematics and Science Center, Room W302
We start by exploring the theme of R-equivalence in algebraic groups. First introduced by Manin to study cubic surfaces, this notion proves to be a fundamental tool in the study of rationality of algebraic group varieties. A k-variety is said to be rational if its function field is purely transcendental over k. We exploit Merkurjev's fundamental computations of R-equivalence classes of adjoint classical groups and give a recursive construction to produce an infinite family of non-rational adjoint groups coming from quadratic forms.\\ \\ In a different direction, we address Serre's injectivity question which asks whether a principal homogeneous space under a linear algebraic group admitting a zero cycle of degree one in fact has a rational point. We give a positive answer to this question for any smooth connected reductive k-group whose Dynkin diagram contains connected components only of type $A_n$, $B_n$ or $C_n$ by relating Serre's question to the norm principles previously proved by Barquero and Merkurjev. \\ \\ The study of norm principles are interesting in their own right and we examine in detail the case of groups of type (non-trialitarian) $D_n$ and get a scalar obstruction defined up to spinor norms whose vanishing will imply the norm principle for them. This in turn will also yield a positive answer to Serre's question for all connected reductive k-groups of classical type.
Tue
04/05/2016
(in 56 days)
4:00pm
Defense: Masters Thesis
Topics in Elliptic Curves: Images of Galois and Selmer groups
Jackson Morrow, Emory University
Contact: Jackson Morrow, jmorro2@emory.edu
Venue: Mathematics and Science Center, Room W304
In this thesis, the author proves theorems on composite level images of Galois for elliptic curves defined over Q. Building on recent work of Rouse, Zureick-Brown, and Zywina, the author finds models for composite level modular curves whose rational points classify elliptic curves over Q with simultaneously non-surjective, composite image of Galois. Also, the author classifies the rational points for almost all of these curves except those of high genus using techniques such as quotients, Chabauty-Coleman methods, etale descent, and associated Prym varieties. Furthermore, the author gives an application of these results to the study of entanglement fields, which play a role in the study of correction factors of various conjectural constants for elliptic curves. The author also proves theorems on bounding the order of p-Selmer groups for twists of elliptic curves defined over number fields. In 1988, Frey provided explicit examples of quadratic twist of elliptic curves over Q with Q-rational points of odd, prime order p whose p-Selmer groups are non-trivial. The author generalizes Frey's result to elliptic curves defined over number fields of small degree using class field theory and also provides explicit examples of elliptic curves over Q, which satisfy our generalized Frey condition.
Tue
04/12/2016
(in 63 days)
4:00pm
Seminar: Algebra
Zeta polynomials for modular form periods (tentative date)
Ken Ono, Emory University
Contact: David Zurieck-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W304
Yuri Manin has been developing a theory of zeta-polynomials, polynomials which are arithmetic geometric in origin which also satisfy a functional equation and the Riemann Hypothesis. He conjectured the existence of such functions for all newforms which arise from critical values of L-functions. We confirm his conjecture by constructing a Bloch-Kato complex using weighted moments of orders of Tate-Shafarevich groups. Surprisngly, for fixed weights, as levels tend to infinity we find these zeta-polynomials converge to Earhart polynomials for classical polytopes. This is joint work with Larry Rolen and Florian Sprung.