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Talks and seminars, possibly part of a conference or series.

The Manin-Peyre's conjectures for an infinite family of projective hypersurfaces in higher dimension

Posted in
Speaker: 
Kevin Destagnol
Organiser(s): 
Université Paris Diderot, Paris 7/MPI
Date: 
Tue, 2017-12-12 14:00 - 15:00
Location: 
MPIM Lecture Hall

For a projective variety containing infinitely many rational points, a
natural question is to count the number of such points of height less
than some bound $B$. The Manin-Peyre's conjectures predict, for Fano
varieties, an asymptotic formula for this number as $B$ goes to
$+\infty$ in terms of geometric invariants of the variety. We will
discuss in this talk the Manin-Peyre's conjectures in the case of the
equation $$x_1y_2y_3\cdots y_n+x_2y_1y_3\cdots
y_n+\cdots+x_ny_1y_2\cdots y_{n-1}=0$$ for every $n \ge 2$.

Feynman diagrams and a spectral sequence for the space of knots

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Speaker: 
Peter Teichner
Affiliation: 
MPIM
Date: 
Mon, 2017-11-20 16:30 - 18:00
Location: 
MPIM Seminar Room
Parent event: 
MPIM Topology Seminar

New guests at the MPIM

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Speaker: 
Sibasish Banerjee, Giordano Cotti, Mark Penney
Date: 
Thu, 2017-11-23 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Algebra up to homotopy

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Speaker: 
Walker Stern
Affiliation: 
MPI
Date: 
Wed, 2017-11-22 16:30 - 18:00
Location: 
MPIM Seminar Room
Parent event: 
IMPRS seminar

Motivic obstruction to rationality of a very general cubic hypersurface in P^5

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Speaker: 
Vladimir Guletskii
Affiliation: 
Liverpool
Date: 
Thu, 2017-11-23 10:30 - 12:00
Location: 
MPIM Seminar Room

Multiplicatively dependent points on curves and applications to algebraic dynamical systems

Posted in
Speaker: 
Alina Ostafe
Affiliation: 
University of New South Wales, Sydney
Date: 
Wed, 2017-12-13 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Bombieri, Masser and Zannier (1999) proved that the intersection of a curve defined over a number
field  with the union of all proper algebraic subgroups of the multiplicative group $\mathbb{G}_m^n$
is a set of bounded height (unless this is false for an obvious reason). It is important to note that this
set is still infinite as the degree of the points is not bounded.
In this talk we present recent results on multiplicative relations of points on algebraic curves, when

The Erdős–Kac theorem

Posted in
Speaker: 
Efthymios Sofos
Affiliation: 
University of Leiden/MPIM
Date: 
Mon, 2017-11-27 14:00 - 15:00
Location: 
MPIM Lecture Hall
The Erdős–Kac theorem states that the number of distinct prime factors of a positive integer n follows
the normal distribution with average loglog(n) and variance loglog(n).A proof via the Central Limit
Theorem will be given.
 

On Lefschetz exceptional collections and quantum cohomology of Grassmannians

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Speaker: 
Maxim Smirnov
Affiliation: 
Universität Augsburg/MPI
Date: 
Thu, 2017-11-30 15:00 - 16:00
Location: 
MPIM Lecture Hall

Given a Lefschetz exceptional collection on a variety $X$ one defines its residual subcategory as
the orthogonal to the rectangular part of the collection. In this talk we will discuss some conjectural
relations between the quantum cohomology of $X$ and the structure of the residual subcategory
motivated by homological mirror symmetry. We give examples of this relation when $X$ is an ordinary
or a symplectic isotropic Grassmannian.

Topological partition functions and (iterated) integrals of modular forms

Posted in
Speaker: 
Jan Manschot
Affiliation: 
Trinigy College Dublin
Date: 
Thu, 2017-11-30 14:00 - 15:00
Location: 
MPIM Lecture Hall

As a consequence of electric-magnetic duality, partition functions of four-dimensional gauge theories
can be expressed in terms of modular forms in many cases. I will discuss new results for the modularity
of topologically twisted partition functions of N=2 and N=4 supersymmetric theories, and in particular
how these partititon functions may involve (iterated) integrals of modular forms.

 

Non-perturbative spectra, quantum curves and mirror symmetry

Posted in
Speaker: 
Andrea Brini
Affiliation: 
CNRS Montpellier/Imperial College
Date: 
Thu, 2017-11-30 11:30 - 12:30
Location: 
MPIM Lecture Hall

"Quantum curves'' have been all the rage for various subsectors of the geometry/mathematical physics community for the last few years; yet they might mean different things for different people. I will focus on one and only one angle of this story, due to Grassi--Hatsuda--Kashaev--Marino--Zakany: in their setting, "quantum curves" is the monicker of a precise connection between the spectral theory of a class of difference operators on the real line with trace-class resolvent, and the enumerative geometry (GW/DT invariants) of toric threefolds with trivial canonical bundle.

Knots-quivers correspondence

Posted in
Speaker: 
Piotr Sulkowski
Affiliation: 
University of Warsaw
Date: 
Thu, 2017-11-30 10:30 - 11:30
Location: 
MPIM Lecture Hall

I will present a surprising relation between knot invariants and quiver representation theory, motivated
by various string theory constructions involving BPS states. Consequences of this relation include the
proof of the famous Labastida-Marino-Ooguri-Vafa conjecture (at least for symmetric representations),
explicit (and unknown before) formulas for colored HOMFLY polynomials for various knots, new
viewpoint on knot homologies, a novel type of categorification, new dualities between quivers,
and many others.

 

Mirror symmetry of branes and hyperbolic $3$-manifolds

Posted in
Speaker: 
Hans Jockers
Affiliation: 
BCTP Bonn
Date: 
Thu, 2017-11-30 09:00 - 10:00
Location: 
MPIM Lecture Hall

We discuss the computation of normal functions between the van Geemen lines on the mirror quintic
Calabi-Yau threefold in a certain semi-stable degeneration limit. In this limit the normal functions are
described as elements of higher Chow groups. Physically this amounts to computing the domain wall
tension between certain B-branes on the mirror quintic in the large complex structure limit. By mirror
symmetry we expect that these normal functions/domain wall tensions have a geometric meaning on the

Analyticity of Gross--Siebert Calabi--Yau families

Posted in
Speaker: 
Helge Ruddat
Affiliation: 
Universität Mainz
Date: 
Wed, 2017-11-29 17:30 - 18:30
Location: 
MPIM Lecture Hall

Gross and Siebert gave an algorithm to produce from toric degeneration data a canonical formal
Calabi--Yau family. Siebert and I prove that this family is in fact the completion of an analytic
family. In particular, its nearby fibres are decent Calabi-Yau manifolds over the complex
numbers. Furthermore, the family is semi-universal, i.e. is in a sense locally the moduli
space of Calabi--Yaus. The key result on the route to analyticity is the computation of canonical
coordinates on the base by explicit integration of a holomorphic volume form over topological

Comparing local and log GW invariants

Posted in
Speaker: 
Michel van Garrel
Affiliation: 
Universität Hamburg
Date: 
Wed, 2017-11-29 16:30 - 17:30
Location: 
MPIM Lecture Hall

Let $X$ be a smooth projective variety and let $D$ be a smooth nef divisor on it. In this collaboration
with Tom Graber and Helge Ruddat, we show that the genus $0$ local Gromov-Witten (GW) invariants
of the total space of $\mathcal{O}(-D)$ equal, up to a factor, the genus $0$ log GW invariants of $X$
with a single condition of maximal contact order along $D$.

Global mirror symmetry

Posted in
Speaker: 
Thomas Reichelt
Affiliation: 
Universität Heidelberg
Date: 
Wed, 2017-11-29 11:30 - 12:30
Location: 
MPIM Lecture Hall

Conjecturally, global mirror symmetry connects the quantum cohomology of projective varieties which
are birational. In this talk, I will focus on the simplest case of a (dis-)crepant blow-up and explain the
construction of the corresponding global Landau-Ginzburg model

Birational geometry of singular symplectic varieties and a global Torelli theorem

Posted in
Speaker: 
Christian Lehn
Affiliation: 
Chemnitz Universität
Date: 
Wed, 2017-11-29 10:30 - 11:30
Location: 
MPIM Lecture Hall

Verbitsky's global Torelli theorem has been one of the most important advances in the theory of holomorphic
symplectic manifolds in the last years. In a joint work with Ben Bakker (University of Georgia) we prove a
version of the global Torelli theorem for singular symplectic varieties and discuss applications. Symplectic
varieties have interesting geometric as well as arithmetic properties, their birational geometry is particularly
rich. We focus on birational contractions of symplectic varieties and generalize a number of known results

Stability data, irregular connections and tropical curves

Posted in
Speaker: 
Sara Angela Filippini
Affiliation: 
Cambridge University
Date: 
Wed, 2017-11-29 09:00 - 10:00
Location: 
MPIM Lecture Hall

I will outline the construction of isomonodromic families of irregular meromorphic connections
on $\mathbb{P}^1$ with values in the derivations of a class of infinite-dimensional Poisson
algebras, and describe two of their scaling limits. In the ``conformal limit'' we recover a version
of the connections introduced by Bridgeland and Toledano-Laredo, while in the ''large complex
structure limit" the connections relate to tropical curves in the plane and, through work of
Gross, Pandharipande and Siebert, to tropical/GW invariants. This is joint work with

Line defects in $\mathcal{N}=2$ QFT and framed quivers

Posted in
Speaker: 
Michele Cirafici
Affiliation: 
IST Lisboa
Date: 
Tue, 2017-11-28 17:30 - 18:30
Location: 
MPIM Lecture Hall

I will discuss a certain class of line defects in four dimensional supersymmetric theories
with $\mathcal{N}=2$. Many properties of these operators can be rephrased in terms of
quiver representation theory. In particular one can study BPS invariants of a new kind, the
so-called framed BPS states, which correspond to bound states of ordinary BPS states with
the defect. Such invariants determine the IR vev of line operators. I will discuss how these
invariants arise from framed quivers. Time permitting I will also discuss a formalism to study

Group actions on quiver varieties and application to branes

Posted in
Speaker: 
Victoria Hoskins
Affiliation: 
Humboldt Universität Berlin
Date: 
Tue, 2017-11-28 16:30 - 17:30
Location: 
MPIM Lecture Hall

We study two types of actions on King's moduli spaces of quiver representations over a
field $k$, and we decompose their fixed loci using group cohomology in order to give
modular interpretations of the components. The first type of action arises by considering
finite groups of quiver automorphisms. The second is the absolute Galois group of a
perfect field $k$ acting on the points of this quiver moduli space valued in an algebraic
closure of $k$; the fixed locus is the set of $k$-rational points, which we decompose

Tropical Hurwitz and GW numbers

Posted in
Speaker: 
Johannes Rau
Affiliation: 
Universität Tübingen
Date: 
Tue, 2017-11-28 11:30 - 12:30
Location: 
MPIM Lecture Hall

Tropical geometry has been proved successful to study various types of enumerative
numbers, including Gromov-Witten invariants for toric surfaces and Hurwitz numbers
with at most two special points. In my talk I will try to give an overview on
some showcase results, recent developments (counting "real'' curves) and relations
to other approaches.

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