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Monday, 9 October | |||
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Time | Speaker | Title | Location |
15:00 - 16:00 |
Nihar Gargava EPFL |
Abstract
In 1945, Siegel showed that the expected value of the lattice-sums of a function over all the lattices of unit covolume in an n-dimensional real vector space is equal to the integral of the function. In 2012, Venkatesh restricted the lattice-sum function to a collection of lattices that had a cyclic group of symmetries and proved a similar mean value theorem. Using this approach, new lower bounds on the most optimal sphere packing density in n dimensions were established for infinitely many n. In the talk, we will outline some analogues of Siegel's mean value theorem over lattices. This approach has modestly improved some of the best known lattice packing bounds in many dimensions. We will speak of some variations and related ideas. (Joint work with V. Serban, M. Viazovska)
Ergodic theory and dynamical systems seminarRandom Arithmetic Lattices as Sphere Packingsread_more |
Y27 H 25 |
15:00 - 16:30 |
Dr. Yalong Cao RIKEN (Japan) |
Abstract
Quivers with potentials are fundamental objects in geometric representation theory and important also in Donaldson-Thomas theory of Calabi-Yau 3-categories. In this talk, we will introduce quantum corrections to such objects by counting quasimaps from curves to the critical locus of the potential. Our construction is based on the theory of gauged linear sigma model (GLSM) and uses recent development of DT theory of CY 4-folds. Joint work with Gufang Zhao.
Algebraic Geometry and Moduli SeminarQuasimaps to quivers with potentials read_more |
ITS |
15:15 - 16:10 |
Fabian Ziltener ETH |
Abstract
This talk is about joint work with Yann Guggisberg. The main result is that the set of generalized symplectic capacities is a complete invariant for every symplectic category whose objects are of the form $(M,\omega)$, such that $M$ is compact and 1-connected, $\omega$ is exact, and there exists a boundary component of $M$ with negative helicity. This answers a question of Cieliebak, Hofer, Latschev, and Schlenk. It appears to be the first result concerning this question, except for results for manifolds of dimension 2, ellipsoids, and polydiscs in $\mathbb{R}^4$.
If time permits, then I will also present some answers to the following question and problem of Cieliebak, Hofer, Latschev, and Schlenk:
Question: Which symplectic capacities are connectedly target-representable?
Problem: Find a minimal generating set of symplectic capacities.
Symplectic Geometry SeminarCapacities as a complete symplectic invariantread_more |
HG G 43 |
16:25 - 17:20 |
Valentin Bosshard ETH |
Abstract
Lagrangian cobordisms induce exact triangles in the Fukaya
category. But how many exact triangles can be recovered by Lagrangian
cobordisms? One way to measure this is by comparing the Lagrangian
cobordism group to the Grothendieck group of the Fukaya category. In this
talk, we discuss the setting of exact conical Lagrangian submanifolds in
Liouville manifolds and compute Lagrangian cobordism groups of Weinstein
manifolds. As an application, we get a geometric interpretation for Viterbo
restriction for Lagrangian cobordism groups.
Symplectic Geometry SeminarThe Lagrangian cobordism group of Weinstein manifoldsread_more |
HG G 43 |
Tuesday, 10 October | |||
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Time | Speaker | Title | Location |
10:30 - 12:00 |
Xenia Flamm Examiner: Prof. Dr. Marc Burger |
HG D 16.2 |
Wednesday, 11 October | |||
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Time | Speaker | Title | Location |
13:30 - 15:00 |
Dr. Johannes Schmitt ETH Zürich |
Abstract
Given a smooth algebraic variety (or orbifold) X with a normal
crossings divisor D, the space X decomposes into strata describing the loci where various components of D (self-)intersect. In this series of four lectures, we will study the intersection theory of X, as well as certain birational modifications of X obtained by iteratively blowing up some of the strata. In recent years, the logarithmic Chow ring of the
pair (X,D) was defined to encode the intersection theory of all such
iterated blow-ups simultaneously. This allows to perform calculations
with strict transforms of cycles on X without specifying a concrete
birational model of X in which they live, and has been applied
successfully in studying certain geometric cycles on moduli spaces.
In the first lecture, we give an overview of the relevant definitions, a sketch of some of their applications, and a roadmap for the following talks. The second lecture talks about the case where X is a toric variety (and D its toric boundary), and explains that here the entire intersection theory is described in terms of convex geometric data (the fan Sigma of X and piecewise polynomial functions on Sigma). Then we show how the language of cone stacks and Artin fans can be used to generalize from the toric situation to arbitrary pairs (X,D). Finally, we talk about ongoing work on the logarithmic Chow ring of the moduli space of curves.
Algebraic Geometry and Moduli SeminarLog intersection theory: from toric varieties to moduli of curves Iread_more |
HG G 43 |
16:30 - 17:30 |
Dr. Théophile Chaumont-Frelet Inria |
Abstract
Time-harmonic Maxwell's equations model the propagation of
electromagnetic waves, and their numerical discretization
by finite elements is instrumental in a large array of applications.
In the simpler setting of acoustic waves, it is known that (i) the Galerkin
Lagrange finite element approximation to a Helmholtz problem becomes
asymptotically optimal as the mesh is refined. Similarly, (ii)
asymptotically constant-free a posteriori error estimates are available
for Helmholtz problems. In this talk, considering Nédélec finite element
discretizations of time-harmonic Maxwell's equations, I will show that
(i) still holds true and propose an a posteriori error estimator providing
(ii). Both results appear to be novel contributions to the existing
literature.
Zurich Colloquium in Applied and Computational MathematicsAsymptotically optimal a priori and a posteriori error estimates for edge finite element discretizations of time-harmonic Maxwell's equationsread_more |
HG E 1.2 |
17:15 - 18:45 |
Prof. Dr. Aleksandar Mijatovic University of Warwick |
Abstract
In this talk we quantify the asymptotic behaviour of multidimensional drifltess diffusions in domains unbounded in a single direction, with asymptotically normal reflections from the boundary. We identify the critical growth/contraction rates of the domain that separate stability, null recurrence and transience. In the stable case we prove existence and uniqueness of the invariant distribution and establish the polynomial rate of decay of its tail. We also establish matching polynomial upper and lower bounds on the rate of convergence to stationarity in total variation. All exponents are explicit in the model parameters that determine the asymptotics of the growth rate of the domain, the interior covariance, and the reflection vector field. Proofs are probabilistic, and use upper and lower tail bounds for additive functionals up to return times to compact sets, for which we develop novel sub/supermartingale criteria, applicable to general continuous semimartingales. Time permitting, I will discuss the main ideas behind the proofs in the talk. This is joint work with Miha Bresar (Warwick) and Andrew Wade (Durham).
Seminar on Stochastic ProcessesBrownian motion with asymptotically normal reflection in unbounded domains: from transience to stabilityread_more |
Y27 H12 |
Thursday, 12 October | |||
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Time | Speaker | Title | Location |
15:00 - 16:00 |
Paula Truölcall_made MPIM Bonn |
Abstract
Algebraic geometry studies solution sets of polynomial equations in multiple variables. For example, an algebraic plane curve is the zero set of a polynomial in two (say, complex) variables. Knot theory, on the other hand, studies 1-dimensional submanifolds of the 3-sphere from a topological perspective - up to continuous deformations. How are these two areas of mathematics related? We will draw connections between knot theory and the study of singularities of algebraic plane curves, assuming no knowledge of either area.
Geometry Graduate ColloquiumRelating knot theory to algebraic geometryread_more |
HG G 19.1 |
17:15 - 18:15 |
Prof. Dr. Benjamin Jourdaincall_made CERMICS |
Abstract
We consider driftless one-dimensional stochastic differential equations. We first recall how they propagate convexity at the level of single marginals. We show that some spatial convexity of the diffusion coefficient is needed to obtain more general convexity propagation and obtain functional convexity propagation under a slight reinforcement of this necessary condition. Such conditions are not needed for directional convexity.
Talks in Financial and Insurance MathematicsConvexity propagation and convex ordering of one-dimensional stochastic differential equationsread_more |
HG G 43 |
Friday, 13 October | |||
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Time | Speaker | Title | Location |
14:15 - 15:15 |
Prof. Dr. William Duke UCLA |
HG G 43 |
|
16:00 - 17:30 |
Dr. Fatemeh Rezaee Cambridge and ETHZ |
Abstract
Let X be a smooth projective variety. Define a stable map f : C → X to be eventually smoothable if there is an embedding X → PN such that (C,f) occurs as the limit of a 1-parameter family of stable maps to PN with smooth domain curves. Via an explicit deformation-theoretic construction, we produce a large class of stable maps (called stable maps with model ghosts), and show that they are eventually smoothable. This is joint work with Mohan Swaminathan.
Algebraic Geometry and Moduli SeminarConstructing smoothings of stable mapsread_more |
HG G 43 |