Localization of locally analytic admissible p-adic representation
Donnerstag, 1.6.17, 09:30-10:30, Strasbourg, IRMA, Salle de conf'erences
(joint work with D. Patel, T. Schmidt, M. Strauch). Let G be a reductive group, Lie(G) its Lie algebra; X the flag variety of G.\n\nIn the complex case, Beilinson-Bernstein and Brylinski-Kashiwara proved in the 80's that there is an equivalence of categories between the central representations of Lie(G) and the D-modules over the flag variety X. In this talk I will explain a p-adic analogous of this theorem. In this case G is a split reductive group, and representations we are considering are the central locally analytic representations of the Qp-points of the group G.\n\nOn the geometric side I will explain how to contruct differential operators over the rigid flag variety of the group G.
p-adic Hodge theory in motivic homotopy
Donnerstag, 1.6.17, 11:00-12:00, Strasbourg, IRMA, Salle de conf'erences
I will present a work in collaboration with Wiesia Niziol which aims to incorporate p-adic Hodge theory into the framework of modules over ring spectra, in the sense of Morel-Voevodsky's motivic homotopy theory. Our main result is the identification of "modules over syntomic cohomology" as a full subcategory of the derived category of potentially semi-stable representations, making use of ideas of Beilinson and Drew. I will then present an ongoing project to extend Fontaine semi-stable comparison to a suitable notion of syntomic modules. The later should be compared to Saito mixed Hodge modules, and our objective is to get some kind of p-adic Riemann-Hilbert correspondence.\n\n
Tate Motives in Representation Theory
Donnerstag, 1.6.17, 14:30-15:30, Strasbourg, IRMA, Salle de conf'erences
A variant of the formalism of\nmotivic sheaves, where the Tate objects\ndo not extend among one another, can explain\nthe phenomenon of graded versions of categories\nof representations underlying the character\nformulas of Kazhdan-Lusztig. This is joint work\nwith Matthias Wendt.
Gluing constructions by singular perturbation methods in Differential Geometry
Donnerstag, 1.6.17, 17:00-18:00, Hörsaal II, Albertstr. 23b
Deep Learning
Freitag, 2.6.17, 12:00-13:00, Raum 404, Eckerstr. 1
Deep learning has been getting large attention in science and the media. In my talk I will show results mainly from computer vision that explain this attention and indicates how things could go on in the future. The talk will consist of three main parts. In the first part, I will give a brief introduction into the fundamentals of deep learning, such as common network architectures and the basic back-propagation algorithm for optimization of their parameters. In the second part, I will show recent results from my group, which developed for the first time learning formulations for 3D computer vision. In the third part, I will list mathematical challenges in deep learning, the solution of which would probably largely improve the state of the art.
Introduction to DNA topology: enzymes that unknot and unlink DNA by local reconnection and local crossing changes
Montag, 5.6.17, 09:00-10:00, Hörsaal Virologie, Hermann-Herder-Straße 11
Classical invariants of knot theory
Montag, 5.6.17, 10:15-11:15, Hörsaal Virologie, Hermann-Herder-Straße 11
Helicity and its role in dynamo theory
Montag, 5.6.17, 11:30-12:30, Hörsaal Virologie, Hermann-Herder-Straße 11
Introduction: regularity of finite energy curves
Montag, 5.6.17, 14:00-15:00, Hörsaal Virologie, Hermann-Herder-Straße 11
Introduction on categorification
Dienstag, 6.6.17, 09:00-10:00, Hörsaal Virologie, Hermann-Herder-Straße 11
Relaxation under topological constraints
Dienstag, 6.6.17, 10:15-11:15, Hörsaal Virologie, Hermann-Herder-Straße 11
Physical Knots
Dienstag, 6.6.17, 11:30-12:30, Hörsaal Virologie, Hermann-Herder-Straße 11
This distinguished lecture series, given by celebrated knot theorist Louis Kauffman from UIC, is a tour of visual ideas relating knots to situations in natural science. We will begin with knots and DNA and the production of knots in DNA recombination. Then we will show a movie of knotted vortices in water (courtesy of the work of William Irvine at the University of Chicago). Irvine and his group accomplished a feat that is the equivalent of blowing a knotted smoke ring! We discuss the possibility of knotted gluon fields in relation to the complexity of knots measured by rope length. We discuss the possibility of framed braids as a basis for elementary particles. And, time permitting, we discuss the pioneering work of Edward Witten on the nature of knot invariants. The lectures are self-contained, open and accessible to students and faculty of sciences.\nNo lower age limit required.
Average crossing number estimates and other corollaries of regularity
Dienstag, 6.6.17, 14:00-15:00, Hörsaal Virologie, Hermann-Herder-Straße 11
The tangle method: Modeling local reconnection using band surgery
Dienstag, 6.6.17, 15:15-16:15, Hörsaal Virologie, Hermann-Herder-Straße 11
Introduction to Knotplot
Dienstag, 6.6.17, 16:30-17:30, Hörsaal Virologie, Hermann-Herder-Straße 11
Why (k)not knots?
Dienstag, 6.6.17, 19:30-20:30, HS 2006 im Kollegiengebäude II
Knotentheorie ist ein faszinierendes und ausgesprochen anschauliches mathematisches Thema an der Schnittstelle der Physik, Mathematik, und Biologie. Professor Kauffman, einer der weltweit führenden Mathematiker auf diesem Gebiet und nicht zuletzt durch seine inspirierenden Vorträge bekannt. Der Vortrag bietet eine Einführung und einen Querschnitt durch die Problemstellungen der modernen Knotentheorie: anschaulich, leicht verständlich und enthusiastisch vorgetragen.\n\n
Minimum energy states of knots and links
Mittwoch, 7.6.17, 09:00-10:00, Hörsaal Virologie, Hermann-Herder-Straße 11
Characterizing finite energy curves
Mittwoch, 7.6.17, 10:15-11:15, Hörsaal Virologie, Hermann-Herder-Straße 11
Physical Knots
Mittwoch, 7.6.17, 11:30-12:30, Hörsaal Virologie, Hermann-Herder-Straße 11
This distinguished lecture series, given by celebrated knot theorist Louis Kauffman from UIC, is a tour of visual ideas relating knots to situations in natural science. We will begin with knots and DNA and the production of knots in DNA recombination. Then we will show a movie of knotted vortices in water (courtesy of the work of William Irvine at the University of Chicago). Irvine and his group accomplished a feat that is the equivalent of blowing a knotted smoke ring! We discuss the possibility of knotted gluon fields in relation to the complexity of knots measured by rope length. We discuss the possibility of framed braids as a basis for elementary particles. And, time permitting, we discuss the pioneering work of Edward Witten on the nature of knot invariants. The lectures are self-contained, open and accessible to students and faculty of sciences.\nNo lower age limit required.
Analysis of DNA packing in viruses using random knotting
Mittwoch, 7.6.17, 14:00-15:00, Hörsaal Virologie, Hermann-Herder-Straße 11
Khovanov link homology
Mittwoch, 7.6.17, 15:15-16:15, Hörsaal Virologie, Hermann-Herder-Straße 11
Physical Knots
Donnerstag, 8.6.17, 11:30-12:30, Hörsaal Virologie, Hermann-Herder-Straße 11
This distinguished lecture series, given by celebrated knot theorist Louis Kauffman from UIC, is a tour of visual ideas relating knots to situations in natural science. We will begin with knots and DNA and the production of knots in DNA recombination. Then we will show a movie of knotted vortices in water (courtesy of the work of William Irvine at the University of Chicago). Irvine and his group accomplished a feat that is the equivalent of blowing a knotted smoke ring! We discuss the possibility of knotted gluon fields in relation to the complexity of knots measured by rope length. We discuss the possibility of framed braids as a basis for elementary particles. And, time permitting, we discuss the pioneering work of Edward Witten on the nature of knot invariants. The lectures are self-contained, open and accessible to students and faculty of sciences.\nNo lower age limit required.
Symmetric critical knots
Freitag, 9.6.17, 09:00-10:00, Hörsaal Virologie, Hermann-Herder-Straße 11
Random linking of minicircles in trypanosomes
Freitag, 9.6.17, 10:15-11:15, Hörsaal Virologie, Hermann-Herder-Straße 11
Topological jumps of minimum area soap-films
Freitag, 9.6.17, 11:30-12:30, Hörsaal Virologie, Hermann-Herder-Straße 11
Quantum invariants of links and 3-manifolds
Freitag, 9.6.17, 14:00-15:00, Hörsaal Virologie, Hermann-Herder-Straße 11
Mirror symmetry of Calabi-Yau manifolds looked from the moduli spaces
Montag, 12.6.17, 16:15-17:15, Raum 404, Eckerstr. 1
Mirror symmetry of Calabi-Yau manifolds was discovered from physics in 90's. Since then, one way to describe the symmetry is to look at suitable moduli spaces of Calabi-Yau manifolds. In this talk, I will start with a brief summary\nof mirror symmetry, and then I will show two interesting examples of Calabi-Yau manifolds given as complete intersections. In these examples, I will observe that\nbirational geometry of Calabi-Yau manifolds are nicely encoded in the moduli spaces of mirror Calabi-Yau manifolds in terms of monodromy properties. In particular, I will identify Picard-Lefschetz type monodromy which corresponds to flops. This is based on collaborations with Hiromichi Takagi.
Geometric analysis on stratified spaces
Dienstag, 13.6.17, 16:00-17:00, Raum 404, Eckerstr. 1
Stratified spaces are singular metric spaces that have been studied from a topological and analytical point of view. In this talk we will give an introduction about this singular setting; we will show how Riemannian geometry can be used to study stratified spaces and how one can obtain geometric and analytic results depending on the positivity of the Ricci curvature.
Stability of lower curvature bounds under \(C0\) deformations of the metric
Dienstag, 13.6.17, 17:00-18:00, Raum 404, Eckerstr. 1
If a sequence of Riemannian manifolds with sectional curvature bounded from below Gromov-Hausdorff converges to a smooth limit manifold, then the limit has sectional curvature bounded from below. This comes from the fact that lower bounds on the sectional curvature have a strong geometric meaning in term of « fatness of geodesic triangles » through Toponogov’s theorem. The aim of this talk is to show how one can deal with other kind of curvature bounds which do not have such a strong geometric flavor (like lower bounds on the curvature operator), at the cost of requiring \(C0\) convergence of the metric instead of Gromov-Hausdorff convergence. This builds up on previous works by Koch-Lamm and Bamler.
Amenability of automorphism groups of generic structures
Mittwoch, 14.6.17, 16:30-17:30, Raum 404, Eckerstr. 1
In a paper by J. Moore following the seminal work of Kechris-Pestov-Todorsevic a correspondence between a certain combinatorial property of a Fraisse class, called convex Ramsey property, and amenability of the automorphism group of the Fraisse limit has been found. In this paper we review similar results for the automorphism groups of generic structures and especially show that automorphism groups of certain generic structures are not amenable by showing that a certain point-line geometries are realized in the generic structure.
Two-block Springer fibers and Springer representations in type D
Freitag, 16.6.17, 10:15-11:15, Raum 404, Eckerstr. 1
We explain how to construct an explicit topological model for\nevery two-block Springer fiber of type D. These so-called topological\nSpringer fibers are homeomorphic to their corresponding algebro-geometric\nSpringer fiber. They are defined combinatorially using cup diagrams which\nappear in the context of finding closed formulas for parabolic\nKazhdan-Lusztig polynomials of type D with respect to a maximal parabolic\nof type A. As an application it is discussed how the topological Springer\nfibers can be used to reconstruct the famous Springer representation in an\nelementary and combinatorial way.
(Localized) learning with kernels
Freitag, 16.6.17, 12:00-13:00, Raum 404, Eckerstr. 1
Using reproducing kernel Hilbert spaces in non-parametric approaches\nfor regression and classification has a long-standing history. In\nthe first part of this talk, I will introduce these kernel-based learning\n(KBL) methods and discuss some existing statistical guarantees for them.\nIn the second part I will present a localization approach that addresses\nthe super-linear computational requirements of KBLs in terms of the number\nof training samples. I will further provide a statistical analysis that\nshows that the "local KBL" achieves the same learning rates as the original,\nglobal KBL. Furthermore, I will report from some large scale experiments\nshowing that the local KBL achieves essentially the same test performance\nas the global KBL, but for a fraction of the computational requirements.\nIn addition, it turns out that the computational requirements for the local\nKBLs are similar to those of a vanilla random chunk approach, while the\nachieved test errors are in most cases significantly better. Finally, if time\npermits, I will briefly explain, how these methods are being made available\nin a recent software package.
Moment maps: from symplectic geometry to G_2 and Spin(7)
Montag, 19.6.17, 16:15-17:15, Raum 404, Eckerstr. 1
After reviewing the classical notions of moment maps in symplectic and hyperkähler geometry, we discuss several generalizations to multisymplectic geometry, where a closed differential form higher degree takes the place of the symplectic form. We describe how these generalizations are related and give further examples for moment maps on manifolds with G_2 or Spin(7)-structures.
The Half-Wave Maps Equation
Dienstag, 20.6.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The half-wave maps equation (HWM) is a newly found geometric evolution equation, which arises as a universal continuum limit for the dynamics of completely integrable spin systems with long-range interactions (also known as Haldane-Shastry and Calogero-Moser models). After a brief summary on the physical background, I will highlight some intriguing mathematical features of (HWM). In particular, I will discuss a complete and explicit classification of its traveling solitary waves and the spectral analysis of the corresponding linearized operator. Finally, I will comment on the close relations and striking differences of (HWM) with the Schrödinger maps equation (Landau-Lisfhitz equation in ferromagnetism) and the wave maps equation (nonlinear sigma model in anti-ferromagnetism).\n
Keller-Segel models coupled to fluid equations.
Dienstag, 20.6.17, 15:15-16:15, Raum 226, Hermann-Herder-Str. 10
We consider chemotaxis equations coupled to the Navier-Stokes equations, which is a mathematical model describing the dynamics of oxygen, swimming bacteria (Bacillus subtilis), and viscous incompressible fluids. It is not known for this model in two and three dimensions whether or not regular solutions exist globally in time or develop a singularity in a finite time, in case that initial data are sufficiently smooth. We discuss existence of regular solutions under a certain type of conditions and asymptotics as well as temporal decays of solutions, as time tends to infinity.
Higher Amalgamation and Finite Covers (of first order structures)
Mittwoch, 21.6.17, 16:30-17:30, Raum 404, Eckerstr. 1
The talk will be about the fine structure of (very) well-behaved complete first order theories.\nTotally categorical structures of disintegrated type (i.e. the underlying strongly minimal set is trivial) can analysed by a chain of finite covers. A finite cover of some structure is an extension by a new sort and new relations such that the old structure is stably embedded (i.e. every automorphism of the old structure extends to the cover) and there is some definable finite-to-one function from the new sort to the\nold sorts. \nNow we have that non-trivial phenomena in this chain of finite covers are connected to something called higher amalgamation, that is the ability to amalgamate certain systems of types. We will investigate higher amalgamation over parameters in a more general setting, i.e. in theories with a good notion of independence (e.g. strongly minimal, stable, simple). We give a general finite cover construction to force failure of higher amalgamation and\napply it to the totally categorical structure (Z/4Z)^\bomega such that higher amalgamation over some parameter fails while it holds over the empty set. \nThis tells us that the analysis of general totally categorical structure via covers has another complication. But on the other hand as we can, after adding a sequence of finite covers, force every omega-categorical theory to have higher amalgamation over any parameter set, we could potentially have a starting point for some sort of classification of general totally categorical theories via covers.\n
Algebraic models of the euclidean plane
Freitag, 23.6.17, 10:15-11:15, Raum 404, Eckerstr. 1
A fake euclidean plane is a real algebraic surface whose complexification has the rational homology type of the plane and whose real locus is diffeomorphic to the euclidean plane, but which is not isomorphic as a real algebraic surface to the affine plane. In this talk, I will give elements of classification of such surfaces up to biregular isomorphisms of real algebraic varieties as well as up to birational diffeomorphisms, that is, algebraic birational maps whose restrictions to the real loci are diffeomorphisms. (Joint work with F. Mangolte (Angers) and J. Blanc (Basel)).
On the Dirac equation in Condensed Matter Physics
Montag, 26.6.17, 16:15-17:15, Raum 404, Eckerstr. 1
The Dirac equation has been widely used to build up \nrelativistic models of particles. Recently it made its (somehow \nunexpected) appearance in Condensed Matter Physics. New two-dimensional \nmaterials possessing Dirac fermions low-energy excitations have been \ndiscovered, the most famous being the graphene (2010 Nobel Prize in \nPhysics awarded to Geim-Novoselov). In this talk I will give an overview \nabout the role of the Dirac operator in some condensed matter systems, \nwith particular emphasis on some models and related analytical \nproblems.
Free homogeneous structures
Mittwoch, 28.6.17, 16:30-17:30, Raum 404, Eckerstr. 1
Free homogeneous structures
Mittwoch, 28.6.17, 16:30-17:30, Raum 404, Eckerstr. 1
A countably infinite first order structure is\nhomogeneous if every isomorphism between finitely generated\nsubstructures extends to a total automorphism. By Fraisse\nTheorem, homogeneous structures arise as the Fraisse limits\nof amalgamation classes. Moreover, a free homogeneous\nstructure is a homogeneous relational structure whose age\nhas the free amalgamation property. In a joint work with\nSolecki, we show that free amalgamation classes has a\n'coherent' form of the extension property for partial\nautomorphisms (EPPA). We further discuss some\ngroup-theoretic consequences of this result on the\nautomorphism group of any free homogeneous structure such\nas the existence of ample generics and a dense locally\nfinite subgroup.
Discrete Geodesic Paths in the Space of Images
Donnerstag, 29.6.17, 17:00-18:00, Hörsaal II, Albertstr. 23b
The space of images will be considered as a Riemannian manifold, where the underlying Riemannian metric simultaneously \nmeasures the cost of image transport and intensity variation, introduced by Trouv{\b’e} and Younes as the metamorphosis model.\nA robust and effective variational time discretization of geodesics paths will proposed and a variational scheme for a time discrete exponential map will investigated.\nThe approach requires the definition of a discrete path energy consisting of a sum of consecutive image matching functionals over a set of image intensity maps and pairwise matching deformations.\nThe talk will present existence and convergence results and discuss applications in image morphing and image animation.\n\n
The Mumford-Tate conjecture for products of K3 surfaces
Freitag, 30.6.17, 10:15-11:15, Raum 404, Eckerstr. 1
The Mumford-Tate conjecture relates the Hodge structure on the singular cohomology of an algebraic variety (over a number field) with the Galois representation on the etale cohomology of that variety. In this talk we explain a new technique that allows us to prove this conjecture for products of K3 surfaces. Along the way we also prove that the system of l-adic realisations of an abelian motive form a compatible system.\n
Computational Models as Drivers of Cardiac Research
Freitag, 30.6.17, 12:00-13:00, Raum 404, Eckerstr. 1
What are models? What is their role in biological research? Can they be relied on? Can computer simulations replace experiments on living animals? When will we have an all-inclusive model of [...insert system of choice...]? Questions like this are frequently raised in professional and lay discussions. This lecture will attempt to address some aspects, using illustrations 'from the heart'.\n