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Autumn Semester 2014
Note: The highlighted event marks the next occurring event and events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.
Date / Time  Speaker  Title  Location  

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19 September 2014 16:1517:00 
Junliang Shen ETH Zürich 
Cobordism invariants of moduli space of stable pairs  HG G 19.1  
Abstract: Abstract: For a compact CalabiYau 3fold, it is well known that the partition function of PandharipandeThomas invariants are rational and satisfies the q ~1/q symmetry. As a generalization, we consider the cobordism invariants obtained by pushing forward the virtual cobordism class of the moduli space to one point. The partition function of cobordism invariants are conjectured to be rational and satisfy a functional equation. I will explain the proof of the rationality for nonsingular projective toric 3fold by descendent theory.  
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24 September 2014 14:0015:00 
Dr. Andrew Morrison ETH Zürich 
Lines on the Fermat quintic (motivically)  HG G 19.2  
26 September 2014 16:0017:00 
Dr. Olivier Fabert VU Amsterdam 
Closedstring mirror symmetry for open manifolds  HG G 43  
Abstract: The classical mirror symmetry conjecture for closed CalabiYau manifolds X and Y relates the rational GromovWitten theory of X with the (extended) deformation theory of complex structures on Y (and vice versa). In my talk I will illustrate how this correspondence is supposed to generalize from closed to open manifolds. The main ingredient is a novel algebraic structure on the symplectic cohomology of an open symplectic manifold, defined by counting Floer curves with arbitrarily many cylindrical ends and varying conformal structure.  
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29 September 2014 16:0017:00 
Dr. Aaron Pixton Harvard University 
A conjectural formula for the double ramification cycle  HG G 19.2  
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30 September 2014 15:1516:15 
Rahul Pandharipande ETH Zürich 
GromovWitten theory, K3 surfaces, and Pixton's conjecture  HG F 26.1  
Abstract: I will discuss new calculations and conjectures made with G. Oberdieck related to the GromovWitten theory of K3 surfaces. A basic connection to Pixton's conjecture on DR cycles will be made and some related directions of inquiry will be pointed out.  
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1 October 2014 14:0015:15 
Dr. Dimitri Zvonkine Jussieu 
Givental's Rmatrix action and Witten's rspin class: explicit computations  HG G 19.2  
Abstract: The GiventalTeleman classification of semisimple cohomological field theories gives a recursive procedure that expresses in terms of tautological classes the Witten rspin class shifted to any point of its Frobenius manifold outside the discriminant. The part of this expression that exceeds the degree of Witten's class gives a family of tautological relations on Mbar_{g,n}. For certain wellchosen points of the Frobenius manifold the recursive procedure can be solved explicitly. We will show the outcome of these computations and the tautological relations thus obtained.  
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1 October 2014 15:3016:45 
Felix Janda ETH Zürich 
rspin relations on the moduli of curves (new connections)  HG G 19.2  
Abstract: By studying the behavior of the GiventalTeleman classification of semisimple cohomological field theories when approaching a nonsemisimple point one can extract tautological relations of the moduli space of stable curves. I want to discuss the example of Witten's rspin class for different r and show recent ideas on how to connect all of them to the 3spin relations.  
3 October 2014 16:0017:00 
Dr. Dimitri Zvonkine Jussieu 
Hurwitz numbers for real polynomials  HG G 43  
Abstract: There are n^{n3} (properly normalized) complex degree n polynomials with n1 fixed critical values. This can be found by establishing a onetoone correspondence between these polynomials and marked trees, which are enumerated by the Cayley formula. The number of (properly normalized) real degree n polynomials with n1 fixed real critical values is equal to the nth EulerBernoulli number. This can be found by establishing a onetoone correspondence between these polynomials and alternating permutations. The problem above can be generalized by allowing multiple critical values and fixing their ramification profiles. In the complex case this problem is solved; in the real case, however, the answer depends on the order of the critical values on the real line. Thus the question arises whether it is possible to attribute a sign to every real polynomial in such a way that the number of polynomials counted with signs is invariant under permutations of critical values. We construct a sign with this property and study the invariant thus obtained. This is joint work with I. Itenberg.  
*
8 October 2014 14:0015:00 
Prof. Dr. Boris Dubrovin SISSA, Trieste 
Quantum integrable systems, symplectic field theory, and Schur polynomials  HG G 19.2  
10 October 2014 16:0017:00 
Dr. Paolo Rossi Université de Bourgogne, France 
Double ramification cycles and quantization of integrable hierarchies  HG G 43  
Abstract: Recently, inspired by symplectic field theory, Alexandr Buryak has defined a new construction of an integrable hierarchy of PDEs associated to a given cohomological field theory. Such construction involves the geometry of the double ramification cycle and, as opposed to SFTtype hierarchies, produces classical dispersive hamiltonian PDEs (among them KdV, ILW and extended Toda). In a joint work in progress we were then able to uncover some interesting properties of such "double ramification hierarchies", including effective recursions for the Hamiltonians and a simple formula for their quantization. In the talk I will present these results and some of their possible applications.  
17 October 2014 16:0017:00 
Prof. Dr. Sergey Shadrin University of Amsterdam 
GromovWitten theory of the projective line  HG G 43  
Abstract: I'll explain how the GromovWitten theory of the projective line fits into the ChekhovEynardOrantin (CEO) topological recursion scheme. It is a byproduct of a more general correspondence between the Givental theory and a local version of the CEO recursion. In the framework of CEO topological recursion physicists suggest a quantization procedure that allows to construct a differential operator called quantum spectral curve that vanishes a socalled wave function obtains as the principle specialization of the corresponding npoint function. In the case of the projective line this general principle appears to work perfectly, and I'll show some very nice combinatorics derived from the semiinfinite wedge formalism that stays behind it.  
24 October 2014 16:0017:00 
Prof. Dr. Matthias Gaberdiel ETH Zürich 
Mathieu Moonshine  HG G 43  
31 October 2014 16:0017:00 
Prof. Dr. Balazs Szendroi Oxford University 
Cohomological DonaldsonThomas theory  HG G 43  
Abstract: I will explain the basics of the cohomological refinement of DonaldsonThomas theory. I will give some sample local computations, and discuss some structures that only exist on cohomological DT. If time permits I will briefly mention an application in quantum cluster theory.  
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12 November 2014 15:1516:15 
Christoph Schiessl ETH Zürich 
Asymptotic behavior of GromovWitten invariants  HG G 19.2  
Abstract: I will discuss the asymptotic behavior of GromovWitten invariants in some concrete examples (P^2, P^3, P^1 x P^1, ...) using the explicit WDVVrelations. This is due to ideas of Itzykon/Francesco and Dubrovin.  
14 November 2014 16:0017:00 
Dr. Benjamin Bakker Humboldt Universität Berlin 
Bounding torsion in geometric families of abelian varieties  HG G 43  
Abstract: A celebrated theorem of Mazur asserts that the order of the torsion part of the group of rational points of an elliptic curve over Q is absolutely bounded; it is conjectured that the same is true for abelian varieties over number fields K, though very little progress has been made in proving it. The natural geometric analog where K is replaced by the function field of a complex curveknown as the geometric torsion conjectureis equivalent to the nonexistence of low genus curves in congruence towers of Siegel modular varieties. In joint work with J. Tsimerman, we prove the geometric torsion conjecture for abelian varieties with real multiplication. We will discuss a general method for ruling out low genus curves in locally symmetric varieties using hyperbolic geometry to bound Seshadri constants and also apply it to some related problems.  
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14 November 2014 17:0018:00 
Prof. Dr. Jim Bryan UBC Vancouver 
DonaldsonThomas theory of local elliptic surfaces via the topological vertex  HG G 43  
Abstract: DonaldsonThomas (DT) invariants of a CalabiYau threefold X are fundamental quantum invariants given by (weighted) Euler characteristics of the Hilbert schemes of X. We compute these invariants for the case where X is a socalled local elliptic surface  it is the total space of the canonical line bundle over an elliptic surface. We find that the generating functions for the invariants admit a nice product structure. We introduce a new technique which allows us to use the topological vertex in this computation  a tool which previously could only be used for toric threefolds. As a by product, we discover surprising new identities for the topological vertex. This is joint work with Martijn Kool, with an assist from Ben Young.  
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19 November 2014 14:0015:00 
Junliang Shen ETH Zürich 
Virtual cobordism classes and Chern numbers  HG G 19.2  
Abstract: Given a projective scheme with a perfect obstruction theory, we get virtual Chern numbers by integrating Chern classes of the virtual tangent bundle against the (Chow) virtual fundamental class. A result by CiocanFontanine and Kapranov says that these numbers actually are the Chern numbers of some integercoefficient cobordism class. We show that this class is just the virtual cobordism class which can be constructed in the corresponding algebraic cobordism group similarly as LiTian and BehrendFantechi. Finally, as an application, we discuss the relation between virtual Chern numbers and descendent invariants in PandharipandeThomas theory. This is related to my talk in September.  
21 November 2014 16:0017:00 
PD Dr. Emanuel Scheidegger Université de Fribourg 
Topological string, Hodge theory and a new Lie algebra  HG G 43  
Abstract: After a review of the Bmodel in topological string theory, we will give a Hodgetheoretic reformulation of the holomorphic anomaly equation and explain a natural Lie algebra structure.  
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26 November 2014 15:3016:30 
Ran Tessler Hebrew Univ. 
Computation of all open genus 0 gravitational descendents  HG G 19.2  
Abstract: We recall the definition of open gravitational descendents in g=0. We then prove a topological recursion relation, which allows us to calculate all open g=0 descendents. Based on a joint work with R. Pandharipande and J. Solomon.  
28 November 2014 16:0017:00 
Dr. Alexander Alexandrov Université de Fribourg 
Open intersection numbers, matrix models and integrability  HG G 43  
Abstract: In my talk I will discuss a family of matrix models, which describes the generating functions of intersection numbers on moduli spaces both for open and closed Riemann surfaces. Linear (Virasoro\Wconstraints) and bilinear (KP\MKP integrable hierarchies) equations follow from the matrix model representation in a standard way.  
*
3 December 2014 14:0016:00 
Prof. Dr. Lothar Göttsche ICTP, Trieste 
Hilbert schemes of points on surfaces  HG G 19.2  
Abstract: In the lecture we review some wellknown facts about Hilbert schemes of points on surfaces: We introduce the Hilbert scheme of points Hilb^n(S) on projective a algebraic surface. These parametrize finite subschemes of length n on S, i.e. generically sets of n points on S. We compute their Betti numbers and introduce the action of the the Heisenberg algebra on the direct sum of the cohomologies of all Hilb^n(S).  
5 December 2014 16:0017:00 
Prof. Dr. Lothar Göttsche ICTP, Trieste 
Refined curve counting: Hilbert schemes, tropical geometry and Fock space  HG G 43  
Abstract: The Severi degrees count the number of plane curves of degree d with delta nodes though d(d+3)/2delta general points. One can study this problem more generally for a linear system on a general algebraic surface. We introduce refined curve counting invariants in two ways: via Hilbert schemes of points and via tropical geometry. For toric surfaces they interpolate between Severi degrees and Welschinger invariants in real algebraic geometry. We use tropical geometry to compute them as vacuum expectation values for some operators on a Fock space.  
12 December 2014 16:0017:00 
Prof. Dr. Marcos Marino Université de Genève 
Spectral theory and mirror symmetry  HG G 43  
Abstract: Recent work in string theory has revealed a surprising connection between the spectral theory of functional difference operators and local mirror symmetry. In this talk, I will give an overview of these developments by focusing on its mathematical consequences. I will associate a functional difference operator to any toric CalabiYau manifold by quantizing its mirror curve, and will state and discuss a precise conjecture expressing the Fredholm determinant of this operator in terms of the enumerative properties of the underlying CalabiYau manifold. 
Organizers: Rahul Pandharipande
Archive: SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11
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