Departement Mathematik

Talks in mathematical physics

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Herbstsemester 2011

Datum / Zeit Referent:in Titel Ort
29. September 2011
15:15-16:15 		Dr. Anton Khoroshkin
ETH Zurich, Switzerland
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Talks in Mathematical Physics

Titel From BV algebras to Frobenius manifolds
Referent:in, Affiliation Dr. Anton Khoroshkin, ETH Zurich, Switzerland
Datum, Zeit 29. September 2011, 15:15-16:15
Ort HG G 43
Abstract The purpose of the talk is to explain that Frobenius manifolds introduced by Dubrovin are in one-to-one correspondence with BV-algebras where the action of BV-operator is trivialized. The equivalence of categories is explained on the level of operads where Frobenius manifolds are considered as algebras over the operad of compactified moduli space of curves. Moreover, this identification provides an explanation of the nature of the Givental group action. A drawback of the construction is the complexity of formulas which become far from useful in particular computations. Based on a joint work with N.Markarian, S.Shadrin.
From BV algebras to Frobenius manifoldsread_more
HG G 43
6. Oktober 2011
15:15-16:15 		Pierre Vogel
Institut de Mathématiques de Jussieu, Paris
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Talks in Mathematical Physics

Titel The exceptional hyperalgebra
Referent:in, Affiliation Pierre Vogel, Institut de Mathématiques de Jussieu, Paris
Datum, Zeit 6. Oktober 2011, 15:15-16:15
Ort HG G 43
Abstract We construct a family of algebras $E_n$ ($n\geq0$) over the polynomial algebra $Q[\alpha,\beta]$ and associative algebra homomorphisms from $E_p\otimes E_q$ to $E_{p+q}$. These algebras are strongly related to the conjectural universal exceptional Lie-algebra ${\cal E}$. More precisely if the Deligne conjecture about this exceptional Lie-algebra is true, each simple $E_n$-module induces a well-defined ${\cal E}$-module. We show that every $E_n$-module induces a representation of the braid group $B_n$. For $n<8$ we prove that $E_n$ is semisimple (over the fraction field $Q(\alpha,\beta)$) and the number of simple $E_n$-modules (up to isomorphism) is 1,1,3,6,15,30,66,98. We conjecture that each $E_n$ is semisimple.
The exceptional hyperalgebraread_more
HG G 43
7. Oktober 2011
10:45-11:45 		Porta Marcello
ETH Zurich
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Talks in Mathematical Physics

Titel Interacting electrons on the honeycomb lattice: a renormalization group analysis
Referent:in, Affiliation Porta Marcello, ETH Zurich
Datum, Zeit 7. Oktober 2011, 10:45-11:45
Ort HIT E 41.1
Abstract In this talk I will present some results on the effect of electron-electron interactions on the low energy Physics of graphene. In the first part of the talk I will discuss the effect of short range interactions on the conductivity of graphene; in fact, for weak interactions, it is possible to rigorously prove that the zero temperature optical conductivity of undoped graphene is universal, that is independent of the interaction and of the hopping parameter. The proof is based on rigorous Renormalization Group methods and Ward identities. Then, in the remaining part of the talk I will consider quantized electromagnetic interactions, by introducing a lattice gauge theory model for graphene. The low energy properties of this model have been investigated order by order in renormalized perturbation theory, and turn out to be dramatically different from the corresponding ones in the short range case; this is due to the fact that electromagnetic interactions are marginal in the RG sense, while short range ones are irrelevant. In particular, the Schwinger functions and the response functions decay with interaction-dependent anomalous exponents. Regarding the two-point Schwinger function, the quasi-particle weight vanishes in the deep infrared, while the effective Fermi velocity flows to the speed of light; concerning the response functions, those associated to a particular distortion of the honeycomb lattice (the "Kekulé" one) or to a particular charge asymmetry between the lattice sites are enhanced with respect to the free case. Joint work with A. Giuliani and V. Mastropietro.
Interacting electrons on the honeycomb lattice: a renormalization group analysisread_more
HIT E 41.1
13. Oktober 2011
15:15-16:15 		Fabio Trova
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Talks in Mathematical Physics

Titel On the Geometric Realization of Dendroidal Sets
Referent:in, Affiliation Fabio Trova,
Datum, Zeit 13. Oktober 2011, 15:15-16:15
Ort HG G 43
Abstract Dendroidal sets have been recently introduced by Moerdijk and Weiss, and extend the theory of simplicial sets to the context of (coloured) operads. In analogy with simplicial sets, there is a notion of a "dendroidal nerve" of an operad, generalising the well known (simplicial) nerve of a category; also, dendroidal sets carry a Quillen model structure, which agrees with Joyal's model structure on simplicial sets. What still lacks is a dendroidal analogue of the geometric realization functor. I will describe a possible approach to this problem, mainly motivated by the works of May and Thomason on infinite loop spaces and spectra. The slogan is that dendroidal sets should be interpreted as "simplicial sets with additional structure", such as $A_\infty$ or $E_\infty$-spaces.
On the Geometric Realization of Dendroidal Setsread_more
HG G 43
20. Oktober 2011
15:15-16:15 		Carl McTague
Max Planck Institute for Mathematics, Bonn
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Talks in Mathematical Physics

Titel The Cayley Plane and String Bordism
Referent:in, Affiliation Carl McTague, Max Planck Institute for Mathematics, Bonn
Datum, Zeit 20. Oktober 2011, 15:15-16:15
Ort HG G 43
Abstract This talk will describe how an affinity between projective spaces and bordism rings extends further than previously known. The known manifestations of this affinity are that real projective bundles generate the unoriented bordism ring; that complex projective bundles generate the oriented bordism ring after inverting 2; and that quaternionic projective bundles almost generate the spin bordism ring after inverting 2---they generate the kernel of the Atiyah invariant. The new manifestation of this affinity which I will describe is that Cayley plane bundles---that is, octonionic projective plane bundles---almost generate string bordism after inverting 6---they generate the kernel of the Witten genus. The key behind this is showing that the divisibility properties of Cayley plane bundle characteristic numbers arising in Borel-Hirzebruch Lie-group-theoretic calculations correspond to the divisibility properties arising in the Hovey-Ravenel-Wilson BP-Hopf-ring-theoretic calculation of string bordism at primes >3.
The Cayley Plane and String Bordismread_more
HG G 43
27. Oktober 2011
15:15-16:15 		Prof. Dr. Francesco Bottacin
Università degli Studi di Padova
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Talks in Mathematical Physics

Titel Closed Differential Forms on Moduli Spaces of Sheaves
Referent:in, Affiliation Prof. Dr. Francesco Bottacin, Università degli Studi di Padova
Datum, Zeit 27. Oktober 2011, 15:15-16:15
Ort HG G 43
Abstract Geometric properties of moduli spaces of sheaves over a smooth projective variety (or K\"ahler manifold) $X$ are often induced by similar properties of $X$ itself. A beautiful example of this general fact was discovered, more then 25 years ago, by Mukai: if $X$ is an algebraic surface endowed with a holomorphic symplectic structure, then a holomorphic symplectic structure can also be constructed on moduli spaces of stable sheaves on $X$. After reviewing Mukai's construction, we shall see how it fits in a much more general framework. Let $X$ be a smooth $n$-dimensional projective variety, and let $Y$ be a moduli space of stable sheaves on $X$. By using the local Atiyah class of a universal family of sheaves on $Y$ we shall construct natural maps $$ f:H^i(X, \Omega_X^j)\longrightarrow H^{k+i-n}(Y, \Omega_Y^{k+j-n}), $$ for any $i,j=1,\dots,n$ and any $k\ge\max\{ n-i,n-j\}$. This gives us a natural way to construct closed differential forms on moduli spaces of sheaves. As an application, we shall describe the construction of closed differential forms on the Hilbert schemes of points of $X$. If $X$ is a Calabi-Yau $n$-fold, our construction can be considered as a higher dimensional generalization of Mukai's result.
Unterlagen beamerfile_download
Closed Differential Forms on Moduli Spaces of Sheavesread_more
HG G 43
1. November 2011
15:15-16:15 		Theo Johnson-Freyd
UC Berkeley
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Talks in Mathematical Physics

Titel Gauge-fixed integrals for Lie algebroids
Referent:in, Affiliation Theo Johnson-Freyd, UC Berkeley
Datum, Zeit 1. November 2011, 15:15-16:15
Ort Y27 H 2
Abstract We describe the ``BRST / Faddeev--Popov gauge-fixing'' definition of integrals on (the quotient stack of) a Lie algebroid. As a central example, we compute the volume of the de Rham stack of a compact manifold. In the process, we find a new proof of the Chern--Gauss--Bonnet theorem. This is joint work with Dan Berwick-Evans.
Unterlagen handoutfile_download
Gauge-fixed integrals for Lie algebroidsread_more
Y27 H 2
3. November 2011
09:00-17:00 		Alberto Cattaneo
University of Zurich
Andras Szenes
University of Geneva
Leonardo Aguirre
ETH Zurich
Ivan Contreras
University of Zurich
Francis Brown
Institut de mathématiques de Jussieu
Zsolt Szilagyi
University of Geneva
Damien Calaque
ETH Zurich
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Talks in Mathematical Physics

Titel Meeting ProDoc Geometry, Algebra and Mathematical Physics
Referent:in, Affiliation Alberto Cattaneo, University of Zurich
Andras Szenes, University of Geneva
Leonardo Aguirre, ETH Zurich
Ivan Contreras, University of Zurich
Francis Brown, Institut de mathématiques de Jussieu
Zsolt Szilagyi, University of Geneva
Damien Calaque, ETH Zurich
Datum, Zeit 3. November 2011, 09:00-17:00
Ort HG G 43
Abstract 09.00-10.00 Alberto Cattaneo (UZH), Classical and quantum Lagrangian field theories with boundary coffee break 10.30-11.30 Andras Szenes (UGE) Cohomology of moduli spaces of flat connections on Riemann surfaces 11.40-12.10 Leonardo Aguirre (ETH) On connections between hyperplane arrangements and representation theory 12.15-12.45 Ivan Contreras (UZH), Integration and Poisson sigma models with boundary lunch 14.00-14.30 Zsolt Szilagyi (UGE), Cohomology of Hilbert scheme via hyperKahler reduction 14.45-15.45 Francis Brown (Jussieu), Modular forms and amplitudes in quantum field theory 16.00-17.00 Damien Calaque (ETH), PBW theorems and a Lie theoretic approach to derived self-intersections
Unterlagen Cattaneo's beamerfile_download
Meeting ProDoc Geometry, Algebra and Mathematical Physicsread_more
HG G 43
10. November 2011
15:15-16:15 		Ajay Ramadoss
ETH Zurich
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Talks in Mathematical Physics

Titel Derived representation schemes and cyclic homology
Referent:in, Affiliation Ajay Ramadoss, ETH Zurich
Datum, Zeit 10. November 2011, 15:15-16:15
Ort HG G 43
Abstract Let A be an algebra over a field k of characteristic 0. It is well known that for any fixed finite dimensional k-vector space $V$, one has the representation scheme Rep(A,V):=Spec(A_V) parametrizing k-algebra homomorphisms from A to End(V). According to the Kontsevich-Rosenberg principle, one expects that structures related to the noncommutative geometry of A induce algebraic-geometric structures on Rep(A,V) for all V. In practise, this works for A formally smooth. In this talk, we shall provide an explicit construction of the derived functor of the functor A -->Rep(A,V) in the sense of nonabelian homological algebra. Our construction makes it possible for us to study the basic properties of the corresponding representation homology. We hope to illustrate basic manifestations of a derived form of the Kontsevich Rosenberg principle. This indicates that representation homology should play the same role in studying the noncommutative geometry of arbitrary algebras that usual representation varieties play in the noncommutative geometry of formally smooth algebras. (Joint with Yuri Berest and (partly) with George Khachatryan)
Derived representation schemes and cyclic homologyread_more
HG G 43
17. November 2011
15:15-16:15 		Douglas Lundholm
IPDE
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Talks in Mathematical Physics

Titel Local exclusion and Lieb-Thirring inequalities for anyons
Referent:in, Affiliation Douglas Lundholm, IPDE
Datum, Zeit 17. November 2011, 15:15-16:15
Ort HG G 43
Abstract We consider the many-particle quantum mechanics of anyons, i.e. identical particles in two space dimensions classified by a continuous statistics parameter alpha in [0,1] ranging from bosons (alpha=0) to fermions (alpha=1). These can be modeled by means of completely symmetric (bosonic) wavefunctions with Aharonov-Bohm topological magnetic potentials attached to every particle. We prove a magnetic Hardy inequality for anyons, which in the case that alpha is an odd numerator fraction implies a local exclusion principle for the kinetic energy of such anyons. From this result, and motivated by the original route to stability of ordinary fermionic matter in three dimensions due to Dyson and Lenard, we prove a Lieb-Thirring inequality for these types of anyons. This is recent joint work with Jan Philip Solovej.
Unterlagen beamerfile_download
Local exclusion and Lieb-Thirring inequalities for anyonsread_more
HG G 43
1. Dezember 2011
15:15-16:15 		Prof. Dr. Hiro Tanaka
Northwestern University
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Talks in Mathematical Physics

Titel A Stable Infinity-Category of Lagrangian Cobordisms
Referent:in, Affiliation Prof. Dr. Hiro Tanaka, Northwestern University
Datum, Zeit 1. Dezember 2011, 15:15-16:15
Ort HG G 43
Abstract In this talk I will discuss a joint project with David Nadler. We construct a category Lag(M), which one can associate to any exact symplectic manifold M. We conjecture that this category is equivalent to a Fukaya category of M, and the result I'll discuss in this talk is that Lag(M) is a stable infinity-category in the sense of Lurie. Some consequences are that Lag(M) is enriched over spectra, and that the homotopy category of Lag(M) is triangulated. We also show that the shift functor, on objects, is equivalent to that of other Fukaya categories in which Lagrangians are graded. Roughly speaking, the objects of Lag(M) are exact Lagrangian submanifolds, and morphisms are cobordisms between them which are Lagrangians in M x T*R. The cobordisms must also be non-characteristic with respect to a Lagrangian skeleton of M. (There are also variations of Lag(M) given by varying the choice of Lagrangian skeleton Lambda.) If time allows, I may also discuss future work, some of which involves computing a Thom spectrum related to (non-compact) Lagrangian cobordisms--this spectrum acts as the `universal coefficients' of Lag(M).
A Stable Infinity-Category of Lagrangian Cobordismsread_more
HG G 43
8. Dezember 2011
15:15-16:15 		Thomas Willwacher
Harvard
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Talks in Mathematical Physics

Titel Homotopy braces formality
Referent:in, Affiliation Thomas Willwacher, Harvard
Datum, Zeit 8. Dezember 2011, 15:15-16:15
Ort HG G 43
Abstract We discuss a recent extension of M. Kontsevich's formality morphism to a homotopy braces, and hence also a homotopy Gerstenhaber morphism.
Homotopy braces formalityread_more
HG G 43
15. Dezember 2011
15:15-16:15 		Camilo Arias Abad
Universität Zürich
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Talks in Mathematical Physics

Titel Reidemeister torsion and de-Rham theorem
Referent:in, Affiliation Camilo Arias Abad, Universität Zürich
Datum, Zeit 15. Dezember 2011, 15:15-16:15
Ort HG G 43
Reidemeister torsion and de-Rham theorem
HG G 43
22. Dezember 2011
15:15-16:15
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Talks in Mathematical Physics

Titel Title T.B.A.
Referent:in, Affiliation
Datum, Zeit 22. Dezember 2011, 15:15-16:15
Ort HG G 43
Title T.B.A.
HG G 43

Organisatoren:innen: Anna Beliakova, Damien Calaque, Alberto Cattaneo, Giovanni Felder, Matthias Gaberdiel, Gian Michele Graf, Horst Knörrer

Archiv: FS 24 HS 23 FS 23 HS 22 FS 22 HS 21 FS 21 HS 20 FS 20 HS 19 FS 19 HS 18 FS 18 HS 17 FS 17 HS 16 FS 16 HS 15 FS 15 HS 14 FS 14 HS 13 FS 13 HS 12 FS 12 HS 11

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