## Anton geraschenko thesis

theories of "topological sigma model" or "Chern-Simons" type, which is well-adapted to quantization in the Batalin-Vilkovisky formalism. The graph-level version is much more subtle, and intimately connected to the "formality" or "quantization" problem for the operad of little n-dimensional disks. I will aim to be elementary, at least in the non-speculative portion of the talk, and I always invite arbitrary questions and interruptions. I will not have time to say anything important, like that this relates the space of conformal blocks for chiral WZW to the Hilbert space for ChernSimons, because I will instead spend too much time being a bit polemical about how to set up the. The properadic / BV / aksz story identifies (modulo combinatorial calculations that are too hard to do by hand, but should be trivial on a correctly-programmed computer) exactly which Poisson structures do admit a wheel-free deformation quantization. ( abstract, handout ) Abstract: A tenet of algebraic topology is that algebraic structures on the homology of a space should correspond to structures at the chain level, such that the axioms that hold on homology are weakened to coherent homotopies. I will discuss two of the most charismatic groups the Conway group Co0 and the FischerGriess Monster group M and explain my calculation that in both cases the anomaly has order exactly.

Lattice Poisson aksz Theory. As with any notes, mine are replete with omissions and errors, undoubtedly; typing does allow me to catch questions from the audience and jokes from the professors, so these are included as well. ( abstract, handout ) Abstract: I will describe two coincidences in homotopy theory, the second a categorification of the first.

If you do too, have a look. Sept 2, Representation Theory, Geometry, and Combinatorics Seminar, UC Berkeley. (aksz theory has already incorporated an analogous step from the geometry of cotangent bundles to the geometry of symplectic manifolds.) The second generalization is to phrase the construction in an algebrotopological language (rather than the usual language of infinite-dimensional smooth manifolds which allows in particular. ( abstract, notes ) Abstract: The method of Feynman diagrams is a well-known example of algebraization of integration. TeX 12 contributions in the last year. I will recall the Koszul duality for properads, and how to compute cofibrant replacements. I will discuss the values of these anomalies, and suggest that often the anomaly of the distinguished "moonshine" action generates the corresponding cohomology group. Abstract: I will describe a version of "T-duality" in which circles are replaced by finite cyclic groups. It assures that the algorithms we teach to undergraduates terminate; it produces Feynman diagrams, the ur-example of "perturbative" physics; and, as I will explain, it also applies to nonperturbative integrals, providing a nonperturbative version of "stationary phase approximation".

Recent developments in noncommutative algebra and related areas, University of Washington. This coincidence, I will argue, is the reason for "unitary" phenomena in physics. Any such action produces an accompanying gauge anomaly living in H4(G;Z). In this talk, based on joint work with Claudia Scheimbauer, I will describe the definition of op)lax natural transformation" between functors of higher categories, and discuss qualitative differences between "lax" and "oplax" twisted quantum field theories.

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