Sunday  Monday  Tuesday  Wednesday  Thursday  Friday  Saturday 
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28 Geometry and Combinatorics
Geometry and Combinatorics Speaker: Ahmed Umer Ashraf (Western) "CSM classes for matroids" Time: 15:30 Room: MC 108 TBA 
29 Quantum Geometry
Quantum Geometry Speaker: Masoud Khalkhali (Western) "Combinatorics of Feynman diagrams and quantum field theory VI" Time: 11:00 Room: MC 108 
30 Geometry and Topology
Geometry and Topology Speaker: Avi Steiner (Western) "Intersection cohomology, characteristic cycles, and affine cones" Time: 15:30 Room: MC 107 Intersection cohomology, invented by Goresky and MacPherson, is a notion of cohomology for singular spaces which admits generalizations of classical theorems such as Poincare duality and the Lefschetz hyperplane theorem. It is constructed by taking global sections of a certain perverse sheaf called the intersection cohomology complex. This complex is itself an interesting topological invariant, and to study it one often looks at its characteristic cycle. In particular, if X is the affine cone over a projective variety Y, one can look at the multiplicity of this cycle over the vertex of X. I will discuss a conjecture of mine which would describe how this multiplicity changes with the projective embedding of Y, along with some evidence for the conjecture being true coming from the normal toric case. 
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1 Algebraic Geometry
Algebraic Geometry Speaker: Nicole Lemire (Western) "Adam's operations and the Gamma Filtration" Time: 15:30 Room: WSC 187 
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4 Geometry and Combinatorics
Geometry and Combinatorics Speaker: (Western) "No talk this week (reading week)" Time: 15:30 Room: MC 108 
5 Quantum Geometry
Quantum Geometry Speaker: Masoud Khalkhali (Western) "Matrix Integrals and Random Matrix Theory" Time: 11:00 Room: MC 108 
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11 Geometry and Combinatorics
Geometry and Combinatorics Speaker: Ahmed Umer Ashraf (Western) "CSM classes of matroids II" Time: 15:30 Room: MC 108 Last time we defined what it means to be a Minkowski weight over a kskeleton of a fan (complete or not). To a loopless matroid, there is an associated simplicial fan called Bergman fan. Following de Medrano, Rincon and Shaw we will define the CSM classes of a loopless matroid as Minkowski weights over this fan. We will show that it satisfies the balancing condition. This will involve some combinatorial machinery concerning matroid that we will review. 
12 Quantum Geometry
Quantum Geometry Speaker: Masoud Khalkhali (Western) "Matrix Integrals and Random Matrix Theory II" Time: 11:00 Room: MC 108 
13 Geometry and Topology
Geometry and Topology Speaker: Luis Scoccola (Western) "Stability of topological invariants of data" Time: 15:30 Room: MC 107 Topological Data Analysis provides a framework for analyzing data that is robust to perturbations of the data. One way in which it accomplishes this is by introducing stable invariants: invariants of data sets that vary continuously with respect to suitable metrics on the collection of data sets. In this talk I will present several well known invariants of different kinds of data (such as metric spaces, metric measure spaces, dynamic metric spaces, and filtered metric spaces) and a theoretical framework that lets us prove known stability results as well as novel ones. 
14 Colloquium
Colloquium Speaker: Sylvie Paycha (Potsdam) "Exploring the geometry of regularity structures" Time: 15:30 Room: MC 108 Regularity structures were introduced by Martin Hairer to deal with the
divergences that arise from stochastic partial differential equations
which typically involve white noise. Exploring the underlying geometry
reveals the role played in this context by direct connections on a
vector bundle. Originally introduced by Nikolai Teleman in the
context of non commutative geometry, these provide a direct transport of
fibres from point to point. We generalise them to groupoids and propose
an interpretation of reexpansion maps arising in regularity structures
in the language of groupoids. Reexpansion maps were introduced by
Hairer to transform a singular stochastic differential equation into a
fixed point problem, based on an ad hoc ``Taylor expansion'' of the
solutions at any point in spacetime and a ``reexpansion map'' which
relates the values at different points. For gauge groupoids, namely
those built from a principal bundle, a reexpansion map can be viewed
as a (local) ``gaugeoid field'', the groupoid counterpart of a (local)
gauge field. We investigate the case of jet bundles arising in
polynomial regularity structures.

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18 Geometry and Combinatorics
Geometry and Combinatorics Speaker: Ahmed Umer Ashraf (Western) "CSM classes for matroids III" Time: 15:30 Room: MC 108 a continuation of last week's talk 
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20 Geometry and Topology
Geometry and Topology Speaker: Daniel FuentesKeuthan (Johns Hopkins University) "Understanding Goodwillie Towers of Infinity Categories" Time: 15:30 Room: MC 107 In a foundational series of papers Goodwillie laid the grounds for a theory of "Taylor Series" for homotopy theory, defining a tower of functors which interpolate between the stable and unstable homotopy type of a functor. Work of Heuts refined this picture by associating to an infinity category a tower of infinity categories which interpolate between the stabilization and the category in a compatible way. Key to the understanding of this tower is a sequence of natural transformations referred to as "Tate diagonals". I will describe some attempts to understand these Tate diagonals, and if time permits some relations between Heuts tower and the homotopy nilpotent groups of Biederman and Dwyer. 
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22 Algebraic Geometry
Algebraic Geometry Speaker: Nicole Lemire (Western) "Adam's operations and the Gamma Filtration" Time: 15:30 Room: WSC 187 
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25 Geometry and Combinatorics
Geometry and Combinatorics Speaker: Graham Denham (Western) "Singular loci of configuration hypersurfaces" Time: 15:30 Room: MC 108 A finite graph determines a Kirchhoff polynomial, which is a
squarefree, homogeneous polynomial in a set of variables indexed by
the edges. The Kirchhoff polynomial appears in an integrand in the
study of particle interactions in highenergy physics, which provides
some incentive to study the motives and periods arising from the
projective hypersurface cut out by such a polynomial. From this perspective, work of Bloch, Esnault and Kreimer (2006)
suggested that the more natural object of study is, in fact, a
polynomial determined by a hyperplane arrangement, which is closely
related to the basis generating polynomial of the associated matroid.
I will describe joint work with Mathias Schulze and Uli Walther on the
singular loci of such polynomials.

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27 Geometry and Topology
Geometry and Topology Speaker: Matthias Franz (Western) "TBA" Time: 15:30 Room: MC 107 
28 Colloquium
Colloquium Speaker: David Bellhouse (Western) "Abraham De Moivre's Normal Approximation to the Binomial" Time: 15:30 Room: MC 108 In 1718 Abraham De Moivre published his Doctrine of Chances, a work on probability theory. Many of the problems solved in the book had been given to him as challenge problems by mathematically inclined friends and patrons. After the book was published, challenge problems continued to flow in. One such problem was given to him by Sir Alexander Cuming in 1721:
Two players of equal skill play ÃƒÂ°Ã‚ÂÃ¢â‚¬ËœÃ¢â‚¬Âº games. At the end of these games, the player who wins the majority of these games gives a spectator a number of units of money corresponding to the difference between the number of games the player has won and ÃƒÂ°Ã‚ÂÃ¢â‚¬ËœÃ¢â‚¬Âº/2. What is the expected amount of money the player is to receive? Cuming also generalized the question to players of unequal skill. De MoivreÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s solution to the original and generalized problem, for large ÃƒÂ°Ã‚ÂÃ¢â‚¬ËœÃ¢â‚¬Âº, is the normal approximation to the binomial, which he obtained in 1733. In this talk, I will give the historical background to the normal approximation to the binomial and De MoivreÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s method of solution, as well as Thomas BayesÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s criticism of the result. 
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