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May 14 to 18, 2012

Monday, May 14
10:15-11:00 Workshop in Coding Theory and Cryptography (uzh)
On Goppa codes on the Hermitian curve and its quotients
Alberto Ravagnani, University of Trento 		Uni Basel
Grosser Hörsaal
Departement Mathematik
Speakers:

Alberto Ravagnani (University of Trento)

11:15-12:00 Workshop in Coding Theory and Cryptography (uzh)
Additively Homomorphic Encryption Revisited: A Framework and (Im-)possibility Results
Andreas Peter, TU Darmstadt 		Uni Basel
Grosser Hörsaal
Departement Mathematik
Speakers:

Andreas Peter (TU Darmstadt)

13:15-14:00 Advanced Seminar in Algebraic Geometry (uzh)
Unirationality of Hurwitz Spaces and Existence of Ulrich Bundles
Dr. Florian Geiss, Universitat des Saarlandes, 		Uni Irchel
Y27 H 25
Speakers:

Dr. Florian Geiss (Universitat des Saarlandes,)

15:15-16:30 Symplectic Geometry Seminar
Hyperkaehler Floer theory, the Fueter equation, and divergence free frames
Dietmar Salamon, ETH Zurich 		ETH Zentrum
HG G 43
Abstract: A divergence free frame on a closed three manifold is called regular if every solution of the linear Fueter equation is constant and is called singular otherwise. The set of singular divergence free frames is an analogue of the Maslov cycle. Regular divergence free frames satisfy an analogue of the Arnold conjecture for flat hyperkaehler target manifolds. The Seiberg-Witten equations can be viewed as gauged versions of the Fueter equation, and so can the Donaldson-Thomas equations on certain seven dimensional product manifolds.
Speakers:

Dietmar Salamon (ETH Zurich)

16:30-18:00 Optimization and Applications Seminar
Vertex Adjacency and the Hirsch Conjecture for the Fractional Stable Set Polytope
Carla Michini, Università di Roma "La Sapienza" 		ETH Zentrum
HG G 19.1
Abstract: Given a graph, the edge formulation of the stable set problem is defi ned by two-variable constraints, one for each edge, expressing the simple condition that two adjacent nodes cannot belong to a stable set. We study the fractional stable set polytope, i.e. the polytope de fined by the linear relaxation of the edge formulation. Even if this polytope is a weak approximation of the stable set polytope, its simple geometrical structure provides deep theoretical insight as well as interesting algorithmic opportunities. Exploiting a graphic characterization of the bases, we first rede fine simplex pivots in terms of simple graphic operations, that turn a given basis into an adjacent one. Between all possible pivots, we characterize degenerate and nondegenerate ones, and we differentiate those leading to an integer or to a fractional vertex. The graphic characterization of bases is crucial to prove another structural property of the fractional stable set polytope, concerning the adjacency of its vertices. In particular, we extend a necessary and sufficient condition due to Chvatal for adjacency of (integer) vertices of the stable set polytope to arbitrary (and possibly fractional) vertices of the fractional stable set polytope. These results lead us to prove that the Hirsch Conjecture is true for the fractional stable set polytope, i.e. the combinatorial diameter of this fractional polytope is at most equal to the number of edges of the given graph. We actually re fine this bound in the nonbipartite case by proving a tighter bound, equal to the number of nodes of the graph. We also design a simplex-like algorithm for the stable set problem that relies on the adjacency properties mentioned above. Our algorithm generates only integer solutions without using cutting plane methods. Preliminary results are encouraging but show that cycling can occur, due to the high degree of degeneracy of the polytope. Nevertheless, the perspective of an exact combinatorial method of solution for the stable set problem based on this algorithm seems intriguing, provided that an anticycling rule is embedded in its current design.
Joint work with Antonio Sassano
Speakers:

Carla Michini (Università di Roma "La Sapienza")

E-Mail:
17:00-19:00 Seminar in Partial Differential Equations (uzh)
Min-max theory of minimal surfaces and the Willmore Conjecture
Prof. Dr. Fernando Coda Marques, IMPA, Brasil 		Uni Irchel
Y27 H 12
Speakers:

Prof. Dr. Fernando Coda Marques (IMPA, Brasil)

 

Tuesday, May 15
15:15-16:15 Analysis Seminar
A Plateau problem for U(1)-bundles in 3 dimensions
Mircea Petrache, ETH Zürich 		ETH Zentrum
HG G 43
Abstract: We will present an analogue of the Plateau problem where possibly singular U(1)-bundles replace 2D surfaces. The main motivation is the search for a variational formulation of Yang-Mills theory in supercritical dimensions, and we present an answer to this quest in the case of abelian structure groups. The relevant closure theorem (analogous to the closure theorem for integral currents) needed in order to apply the direct method of the calculus of variations is proven by a slicing argument as in Ambrosio-Kirchheim and Hardt-Riviere.
The regularity theory for minimizers utilizes instead a new combinatorial argument based on the max-flow min-cut theorem and relies on Smirnov's decomposition of 1-currents.
Speakers:

Mircea Petrache (ETH Zürich)

17:15-18:30 Zurich Graduate Colloquium (uzh)
What is... The Riemann Hypothesis?
Andreas Steiger, ETHZ 		Uni Zentrum
KO2 F 150
Speakers:

Andreas Steiger (ETHZ)

 

Wednesday, May 16
13:00-15:00 FIM Minicourse
Stochastic Variational Analysis
Prof. Dr. Roger Wets, University of California, Davis, USA 		ETH Zentrum
HG G 43
Abstract: Stochastic Variational Analysis“ emerged in response to the need of solving (generalized) equations systems, optimization and variational problems whose parameters are, in part, stochastic. Problems of this type arise in stochastic optimization, stochastic equilibrium problems, uncertainty quantification, statistical estimation problems that turn up in a broad variety of engineering, economics, finance, energy networks, signal processing, ecology and biological problems. These lectures will be introductory in nature, and as much as time will allow, will concentrate on applications. Because the solutions to such systems aren‘t generally unique, one can‘t rely on classical probabilistic techniques to either describe their solutions or find (probabilistic) approximations that might, in turn, be based on standard laws of large numbers and associated asymptotic analysis. The foundations of the theory lie in an understanding of the geometry and the analytic (topological) properties of random sets, including a suitable translation to a functional setting, coupled with both appropriate laws of large numbers, i.e., what can be learned from large samples, and fundamental inequalities, i.e., what can be learned from small samples. This dual approach is fundamental to the potential applications of the theory in practical settings.
Speakers:

Prof. Dr. Roger Wets (University of California, Davis, USA)

14:00-15:00 Talks in Mathematical Physics
Manin triples twist and co-ideal algebras
Samuel Beliard, Montpellier 2 		ETH Hönggerberg
HIT E 41.1
Abstract: The algebraic structures that lead to the integrability of quantum integrable models are given by quantum groups (for models on a line or on a circle) and by coideal algebras (for models on a segment or on a half-line).Quantum groups can be constructed from the quantification of Universal enveloping Lie algebras. This procedure, introduced by Drinfel'd in 1985, uses the notion of bialgebras or equivalently of Manin triples. In a recent paper, (arxiv:1202.2312 in collaboration with N. Crampé) we introduced the notion of Manin triples twist and gave a procedure to construct coideal algebras from Universal enveloping Lie sub-algebras. We will review Drinfel'd quantification procedure and present our quantification procedure to obtain coideal algebras. Some applications to quantum integrable models will be discussed.
Speakers:

Samuel Beliard (Montpellier 2)

15:00-15:45 Advanced Seminar in Algebraic Geometry (uzh)
Harder-Narasimhan stratifications and moduli of unstable sheaves
Dr. Victoria Hoskins, Leibniz Universitat Hannover 		Uni Irchel
Y27 H 46
Speakers:

Dr. Victoria Hoskins (Leibniz Universitat Hannover)

15:00-16:00 FIM Announcements
FIM Tea 		ETH Zentrum
HG G 69
15:45-16:45 Geometry Seminar
Aperiodic sequences and aperiodic geodesics
Steffen Weil, Universität Zürich 		ETH Zentrum
HG G 43
Abstract: We will introduce a quantitative condition on orbits of a compact dynamical system which measures aperiodicity. This condition will be discussed concretely for the examples of the Bernoulli-shift and the geodesic flow on compact hyperbolic manifolds. Thereby we will show the existence of special aperiodic sequences and geodesics which are, in some sense, as aperiodic as possible.
This is joint work with V. Schroeder.
Speakers:

Steffen Weil (Universität Zürich)

17:15-18:15 Seminar on Stochastic Processes
A panoramic view of the Uniform Infinite Planar Quadrangulation
Nicolas Curien, Ecole Normale Supérieure, Paris 		UZH Irchel
Y27 H 25
Abstract: The purpose of this talk is to present and study the Uniform Infinite Planar Quadrangulation (UIPQ), which is a model of random discrete planar geometry consisting in a cell decomposition of the plane into quadrangles, chosen "uniformly at random" among all homeomorphically distinct possibilities. We will present a construction of the UIPQ based on well-labeled trees, study some of its amazing properties, and link this object to the Brownian Map of Le Gall and Miermont. Based on joint works with Itai Benjamini, Jean-François Le Gall, Laurent Ménard & Grégory Miermont.
Speakers:

Nicolas Curien (Ecole Normale Supérieure, Paris)

 

Thursday, May 17
08:00-18:00 FIM Announcements
Public Holiday: Ascension Day

 

Friday, May 18
13:00-14:30 Numerics Seminar (uzh)
On Black-Scholes equation and option pricing
Dr. Ivana Kosirova, Universität Zürich 		Uni Irchel
Y27 H 12
Speakers:

Dr. Ivana Kosirova (Universität Zürich)

14:00-15:00 Talks in Financial and Insurance Mathematics
Optimal Order Placement
Prof. Dr. Peter Bank, TU Berlin 		ETH Zentrum
HG G 19.1
Abstract: The execution of large transactions on a financial market will typically affect market prices in an adverse manner, thus leading to possibly significant execution costs. Minimizing these costs requires to trade-off projections of future market depth vs. market resilience and vs. the urgency to trade. We present an extension of the model proposed by Obizhaeva and Wang which allows for these key market parameters to change over time and we show how to produce a closed-form solution to the resulting optimal control problem. (This is joint work with Antje Fruth.)
Speakers:

Prof. Dr. Peter Bank (TU Berlin)

14:15-15:15 Number Theory Seminar
Computing coefficients of modular forms
Dr. Peter Bruin, Universität Zürich 		ETH Zentrum
HG G 43
Abstract: We consider normalised Hecke eigenforms of weight k and level n. In recent years, Edixhoven, Couveignes et al. (for n = 1) and the speaker (generalisation to n ≥ 1) developed an algorithm that, given such an f and an integer m ≥ 1 in factored form, computes the m-th coefficient of the q-expansion of f in time polynomial in n, k and log m under the generalised Riemann hypothesis. I will describe this algorithm and explain some of the ingredients needed to prove its correctness.
Speakers:

Dr. Peter Bruin (Universität Zürich)

16:00-17:00 Algebraic Geometry and Moduli Seminar
Operational K-theory and localization for toric varieties
Prof. Dr. Sam Payne, Yale / MPI Bonn 		ETH Zentrum
HG G 43
Abstract: The Grothendieck rings of ordinary and equivariant vector bundles on a
smooth complete toric variety are well-understood and can be described
through localization in terms of ``piecewise Laurent polynomials";
this is the K-theory analogue of the standard description of the
cohomology rings in terms of piecewise polynomials on fans. A
satisfactory understanding of Grothendieck rings of vector bundles on
singular toric varieties, however, remains out of reach.

I will discuss joint work with Dave Anderson exploring an
``operational equivariant K-theory" that agrees with the Grothendieck
ring of equivariant vector bundles on a smooth variety with torus
action and can be described in terms of localization and piecewise
polynomials on an arbitrary singular toric variety.
Speakers:

Prof. Dr. Sam Payne (Yale / MPI Bonn)

 

Saturday, May 19
No events scheduled today!
No events scheduled today!

 

 

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