"Connected sum constructions in geometry and nonlinear analysis " (Frank Pacard's Note) Teil 2
Dienstag, 4.6.13, 16:15-17:15, Raum 404, Eckerstr. 1
Generalized random forcing for weakly compact
Mittwoch, 5.6.13, 16:30-17:30, Raum 404, Eckerstr. 1
On the invariant universality property
Donnerstag, 6.6.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
The notion of Borel reducibility has been introduced as a tool for measuring the\ntopological complexity of analytic equivalence relations and quasi-orders, an abstract class of\nobjects which includes many relations from various areas of mathematics such as: isomorphism and\n(algebraic) embeddability between countable structures from model theory, homeomorphism and\ntopological embeddability between continua from general topology, isometry and isometric\nembeddability between Polish spaces from analysis, linear isometry and linear isometric\nembeddability between separable Banach spaces from functional analysis, and many others.\nIntuitively, an analytic quasi-order as above is called invariantly universal if it contains in a\nnatural way a Borel-isomorphic copy of any other analytic quasi-order. In this talk, building on\nprevious work of Louveau and Rosendal we will show that most of the analytic quasi-orders which\nare sufficiently complicated (that is: Borel-complete) are in fact invariantly universal. For\nexample, one can show that for every analytic quasi-order R there is a Borel collection C of\nseparable Banach spaces closed under linear isometry such that the relation of linear isometric\nembeddability on C is Borel-isomorphic to R.\n
Dimer models and toric geometry
Montag, 10.6.13, 16:15-17:15, Raum 404, Eckerstr. 1
"Connected sum constructions in geometry and nonlinear analysis " (Frank Pacard's Note) Teil 3
Dienstag, 11.6.13, 16:15-17:15, Raum 404, Eckerstr. 1
On Limitations of the Ehrenfeucht-Fraïssé method
Mittwoch, 12.6.13, 16:30-17:30, Raum 404, Eckerstr. 1
Donnerstag, 13.6.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Mathematical Immunology - Using mathematical models to understand infection and immune dynamics
Freitag, 14.6.13, 11:30-12:30, Raum 404, Eckerstr. 1
Interpreting experimental and clinical data with mathematical models and bioinformatical tools represents a new field in biology to reveal mechanisms of interaction between pathogens and immune cells during infection. This methodology helped substantially in understanding the quantitative and mechanistic aspects of viral and immune dynamics. For instance, it allowed us to estimate the lifetime of immune memory cells, or to determine the replication dynamics of human immunodeficiency virus (HIV).\n\nIn this talk, I will give a brief overview of the field of mathematical immunology with its various applications and results. In particular, I will show how we have used different tools to understand the role of a specific type of immune cells, so called CD8+ T cells, during persistent viral infections, as they are for example caused by HIV or hepatitis C virus.
TBA
Montag, 17.6.13, 16:15-17:15, Raum 404, Eckerstr. 1
The elliptic genus of K3
Montag, 17.6.13, 16:15-17:15, Raum 404, Eckerstr. 1
Elliptic genera have been introduced and studied in the late 80s, on the one hand in topology in the context of circle actions on manifolds, and on the other hand in physics in the context of Dirac-like operators on loop spaces. The elliptic genus of a Calabi-Yau manifold X is a modular function which interpolates between some of the known topological invariants of X. A two-variable version of the elliptic genus was suggested by Witten in the mid 90s, which most naturally arises as an invariant of superconformal field theories associated to X, and which encorporates almost all other versions of the elliptic genus as specializations. The precise relations between the conformal field theorists' and the topologists' approaches to the elliptic genus have subsequently been clarified by Malikov/Schechtman/Vaintrob, by Borisov/Libgober, and by Kapustin.\n\n\nThe talk will first give an overview on the construction of the elliptic genus for Calabi-Yau manifolds X. Then specific properties of the elliptic genus for K3 surfaces X will be discussed, including a number of open conjectures related to the so-called "Mathieu Moonshine Phenomenon" for the elliptic genus of K3.
Numerical Resolution of Conservation Laws on Graphic Cards
Dienstag, 18.6.13, 11:00-12:00, Raum 226, Hermann-Herder-Str. 10
We present several numerical simulations of conservation laws on recent multicore processors, such as GPUs, using the OpenCL programming framework. Depending on the chosen numerical method, different implementation strategies have to be considered, for achieving the best performance. We explain how to program efficiently several methods: a finite volume approach on a structured grid, a high order Discontinuous Galerkin (DG) method on an unstructured grid and a Particle-In-Cell (PIC) method. The three methods are respectively applied to a two-fluid computation, a Maxwell simulation and a Vlasov-Maxwell simulation.
Analytical and Numerical Methods in Shape Optimization
Dienstag, 18.6.13, 14:00-15:00, Raum 226, Hermann-Herder-Str. 10
Shape optimization is quite indispensable for designing and\nconstructing industrial components. Many problems that arise in application, particularly in structural mechanics and in the optimal control of distributed parameter systems, can be formulated as the minimization of functionals defined over a class of admissible domains.\n\nThe present talk aims at surveying on shape optimization.\nEspecially, the following items will be addressed:\n\n- analysis of shape optimization problems,\n\n- the discretization of shapes,\n\n- first and second order shape optimization methods,\n\n- existence and convergence of approximate shapes,\n\n- efficient numerical techniques to compute the state equation.
Heyting algebras
Mittwoch, 19.6.13, 16:30-17:30, Raum 404, Eckerstr. 1
Forschen als Post-Doc
Mittwoch, 19.6.13, 19:15-20:15, Raum 404, Eckerstr. 1
Donnerstag, 20.6.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Newton-Okounkov bodies, vanishing sequences, and diophantine approximation
Freitag, 21.6.13, 10:00-11:00, Raum 404, Eckerstr. 1
We will study global sections of line bundles on projective varieties. Newton-Okounkov bodies are a useful tool for handling all global sections of all multiples of a given line bundle at the same time via convex geometry in Euclidean spaces. We go one step further and study functions on Newton-Okounkov bodies that come from valuations on the underlying function field. It turns out that a variation of this theme \nhas led McKinnon and Roth to very interesting results in diophantine approximation. This is an account of joint work with Sebastien Boucksom, Catriona Maclean, and Tomasz Szemberg.
The Topological eta-Invariant
Montag, 24.6.13, 16:15-17:15, Raum 404, Eckerstr. 1
The Topological eta-Invariant
Montag, 24.6.13, 16:15-17:15, Raum 404, Eckerstr. 1
The eta-invariant can be defined on twisted Dirac-operators over Spin^c-manifolds and it fulfills certain index-theorems. First, the talk will show a way to derive a bordism invariant from these theorems and, second, use the Pontrjagin-Thom construction and homotopy theory to construct a bordism invariant by topological means. The talk will state that the two invariants coincide, but won't prove this statement.
Inner Models for Set Theory Defined by Generalized Logics
Mittwoch, 26.6.13, 16:30-17:30, Raum 404, Eckerstr. 1
Some Reflections on the Continuum Hypothesis
Donnerstag, 27.6.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
The Continuum Problem is whether there is a set of reals whose cardinality is\nstrictly between the cardinality of the integers and the reals. This was the first\nproblem on Hilbert’s famous list and it turned out to be undecidable by the usual\naxiom systems for Set Theory. The results of Goedel and Cohen tell us that the\naxioms give very little information about the relative size of the set of integers and\nthe set of reals. Goedel’s conjecture that strong axioms of infinity will settle the\nproblem turned out to be false. Is this the end of the story?\nIn this talk we shall survey some of current approaches of trying to give a mean-\ningful answer to the problem, in spite of its independence. Two direction of research\nwe shall concentrate on will be forcing axioms and the theory of universally Baire\nsets of reals.\n
Homological smoothness of equivariant derived categories
Freitag, 28.6.13, 10:00-11:00, Raum 404, Eckerstr. 1
We introduce the notion of (homological) G-smoothness for a complex G-variety X. If there are only finitely many G-orbits and all stabilizers are connected, we show that X is G-smooth if and only if each orbit is isomorphic to C^n.