Homotopy theory of singular foliations
Montag, 3.2.20, 14:30-15:30, Raum 414, Ernst-Zermelo-Str. 1
Chiral Conformal Field Theory and Vertex Operator Algebras
Montag, 3.2.20, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
Conformal Field Theory (CFT) is a branch of mathematical physics with many intriguing\napplications, the most mathematically fruitful of which (to date) has been Moonshine Theory.\nIn physics, CFT plays major roles in the treatment of critical phenomena, String Theory\nand AdS/CFT correspondence.\n\nIn the first part of this talk, I will give a short introduction to unitary two dimensional\nEuclidean CFTs (in contrast to relativistic QFTs), before truncating them to so called ‘chiral’\nCFTs. One crucial element of CFT is the so-called Operator Product Expansion (OPE),\nwhich is, in the chiral context, encoded in the structure of a conformal Vertex Operator\nAlgebra (VOA). As an elementary (yet useful) example, the \nU(1) current of the free boson\nwill be considered and I will show how it fits into a conformal VOA.
wird noch bekanntgegeben
Dienstag, 4.2.20, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
On the mean field limit of the Doi-Onsager model for liquid crystals
Dienstag, 4.2.20, 16:00-17:00, Raum 404, Ernst-Zermelo-Str. 1
The microscopic Doi-Onsager model is one of the most fundamental theories for liquid crystals. Formally, one can derive the macroscopic liquid crystals theories such as the Oseen-Frank/Ericksen-Leslie theory from it. We will discuss this issue in a rigorous framework. In particular, we show that when the typical molecular interaction distance tends to zero (called the mean field limit), minimizers or critical points of Onsager's energy functional converge to minimizing harmonic maps or weak harmonic maps respectively. If time permits, we will also show that, under the same limit, solutions of the dynamical Doi-Onsager equation without hydrodynamics will converge to weak solutions of the harmonic map heat flow, which can be viewed as a special Oseen-Frank gradient flow. These are based on joint works with Yuning Liu (NYU Shanghai).
Invariant generalized geometry on maximal flag manifolds
Dienstag, 4.2.20, 16:15-17:15, Fakultätssitzungsraum (4.OG)
The purpose of this talk is to describe the set of generalized complex structures on a maximal flag manifold which are invariant by the adjoint action on the flag, as well as study some of their geometric properties. We will give an explicit expression for the invariant pure spinor line associted with each of these structures. We will characterize all invariant generalized Kähler structures on a maximal flag manifold. Finally, we will describe the quotient spaces determined by the set of all invariant generalized complex (resp. almost Kähler) structures under the action by invariant B-transformations. This is a joint work with Elizabeth Gasparim and Carlos Varea.
Torsion orders of Fano hypersurfaces
Freitag, 7.2.20, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
We find new lower bounds on the torsion orders of very general Fano hypersurfaces over (uncountable) fields of arbitrary characteristic. Our results imply that unirational parametrizations of most Fano hypersurfaces need to have enormously large degree. Our results also hold in characteristic two, where they solve the rationality problem for hypersurfaces under a logarithmic degree bound, thereby extending a previous result of the speaker from characteristic different from two to arbitrary characteristic.
Transfer Operator Approach to Selberg's Zeta Function
Montag, 10.2.20, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
The Selberg zeta function is a central object in the study of correlations between spectral and geometric data on hyperbolic orbifolds. Motivated by D. Mayer's seminal investigations of the modular surface, one promising approach relies on a representation of the zeta function as a Fredholm determinant of certain, purpose-built, transfer operators associated with the geodesic flow on the orbifold. In particular, this representation yields a correspondence between the 1-eigenspaces of these operators and zeros of the zeta function, which in turn relate to \(L^2\)-eigenvalues and resonances of the Laplacian.\nBased on previous work by A. Pohl and various coauthors, we construct such transfer operator families for a wide class of geometrically finite Fuchsian groups with hyperbolic ends, as well as Banach spaces on which these operators act nuclearly of order 0. This is work in progress, jointly with A. Pohl.
Existence theory for generalized Navier-Stokes Equations with pseudomonotone operators
Dienstag, 11.2.20, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We apply pseudomonotone operator theory to the steady generalized Navier-Stokes Equations for shear-thinning fluids. In the homogeneous case, existence will be proved without additional assumptions. When transferring that proof to the inhomogeneous situation, technical difficulties will arise and be solved with the aid of posing smallness and regularity conditions on the data.\n\n
Parabolic Higgs Bundles and Gravitational Instantons
Mittwoch, 12.2.20, 16:15-17:15, Hörsaal II, Albertstr. 23b
Festkolloquium zur Emeritierung von Prof. Dr. Dietmar Kröner
Donnerstag, 13.2.20, 13:30-14:30, Hörsaal II, Albertstr. 23b
Festkolloquium zur Emeritierung von Prof. Dietmar Kröner
Donnerstag, 13.2.20, 13:30-14:30, Hörsaal II, Albertstr. 23b
Donnerstag, 13.2.20, 17:00-18:00, Hörsaal II, Albertstr. 23b
Donnerstag, 13.2.20, 17:00-18:00, Hörsaal II, Albertstr. 23b
Kolloquium zum Abschied von Prof. Kröner
On the Zilber-Pink Conjecture for complex abelian varieties
Freitag, 14.2.20, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
The Zilber-Pink conjecture roughly says that the intersection of a subvariety of an abelian variety with its algebraic subgroups of large enough codimension is well behaved. In the case the subvariety has dimension 1, if the abelian variety and the subvariety are defined over the algebraic numbers, Habegger and Pila proved the conjecture, thus showing that the intersection of a curve with algebraic subgroups of codimension at least 2 is finite, unless the curve is contained in a proper algebraic subgroup. Together with Gabriel Dill, using a recent result of Gao, we extended this statement to complex abelian varieties. More generally, we showed that the whole conjecture for complex abelian varieties can be deduced from the algebraic case.\n
Applications of Lie theory to Symplectic Geometry
Dienstag, 25.2.20, 14:15-15:15, Raum 404, Ernst-Zermelo-Str. 1
I will explain a construction of symplectic Lefschetz fibrations on \nadjoint orbits, give examples and an application to mirror symmetry. \nI will then show that our construction produces a family of examples \nsatisfying the Kontsevich-Katzarkov-Pantev conjecture \n(this is joint work with Ballico, San Martin, and Rubilar).
Nichts über uns - ohne uns
Donnerstag, 27.2.20, 10:15-11:15, Veranstaltungssaal UB, 1. OG
Pressemitteilung Inklusionstag 2020\n\nVeranstaltungshinweis:\n\nIm Rahmen des Inklusionstages 2020 kommt der Aktivist für Inklusion und Barrierefreiheit Raul Krauthausen am 27.02.2020 an die Albert-Ludwigs-Universität Freiburg. \n\nAls Rollstuhlfahrer weiß er, wie wichtig eine barrierefreie und inklusive Gesellschaft ist. Aus diesem Grund engagiert er sich täglich für diese Themen. Wir freuen uns auf seinen Vortrag „Nichts über uns - ohne uns“ in dem er auf Themen rund um die Inklusion eingeht.\n\nAnschließend findet eine Podiumsdiskussion statt. Teilnehmer: Kanzler Dr. Matthias Schenek , Raul Krauthausen, Ramon Kathrein (Stadtrat der Stadt Freiburg) sowie Zeno Springklee von Studieren ohne Hürden (SoH)\n\nDie universitätsoffene Veranstaltung findet am 27.02.2020 ab 10.15 Uhr in der Universitätsbibliothek, Veranstaltungssaal, 1.OG statt.
Interpolating stringy geometry: from Spin(7) and G_2 to Virasoro N=2
Donnerstag, 27.2.20, 14:15-15:15, Raum 404, Ernst-Zermelo-Str. 1
Spectral flow, topological twists, chiral rings related to a refinement of the de Rham cohomology and to marginal deformations, spacetime supersymmetry, mirror symmetry. These are some examples of features arising from the N=2 Virasoro chiral algebra of superstrings compactified on Calabi-Yau manifolds. To various degrees of certainty, similar features were also established for compactifications on 7- and 8-dimensional manifolds with exceptional holonomy group G2 and Spin(7) respectively. In this talk, I will explain that these are more than analogies: I will discuss the underlying symmetry connecting exceptional holonomy to Calabi-Yau surfaces (K3) via a limiting process. Based on arXiv:2001.10539.