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28 Transformation Groups Seminar
Transformation Groups Seminar Speaker: Steven Amelotte (Western) "Cohomology operations for momentangle complexes and minimal free resolutions of StanleyReisner rings" Time: 09:30  11:00 Room: MC 107 After reviewing some results from last week's talk concerning momentangle complexes $\mathcal{Z}_K$ and their cohomology rings, I will describe some further structure on $H^*(\mathcal{Z}_K)$ given by cohomology operations induced by the standard torus action. Under the identification of $H^*(\mathcal{Z}_K)$ with the Koszul homology of the StanleyReisner ring of $K$, these operations assemble to give an explicit differential on the minimal free resolution of the StanleyReisner ring. Using this topological interpretation of the minimal free resolution, we give simple algebraic and combinatorial characterizations of equivariant formality for torus actions on momentangle complexes. This is joint work with Benjamin Briggs. Analysis Seminar
Analysis Seminar Speaker: Blake J. Boudreaux (Western) "Rational Convexity of Totally Real Sets" Time: 14:30  15:30 Room: MC 107 A compact set $X\subset\mathbb C^n$ is said to be rationally convex if for every point $z\not\in X$ there is a polynomial $P$, depending on $z$, so that $P(z)=0$ but $P^{1}(0)\cap X=\varnothing$. In view of the OkaWeil theorem, any function holomorphic on a rationally convex compact $X$ can be approximated uniformly on $X$ by rational functions with poles off $X$. A totally real manifold $M$ is one whose tangent space has no complex structure, i.e., $J(T_pM)\cap T_pM=\{0\}$ for all $p\in M$.
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By a classical result of DuvalSibony, a totally real manifold $M$ in $\mathbb{C}^n$ is rationally convex if and only if there exists a KÃƒÂ¤hler form $dd^c\varphi$ for which $M$ is isotropic. Under a mild technical assumption, we generalize this necessary and sufficient condition to the setting of totally real sets (zero loci of strictly plurisubharmonic functions). 
29 Basic Notions Seminar
Basic Notions Seminar Speaker: Taylor Brysiewicz (Western) "Basic Notions: Numerical Algebraic Geometry" Time: 15:30  16:30 Room: MC 107 Numerical algebraic geometry is a computational framework for studying solution sets to polynomial equations (called varieties) using numerical algorithms. In contrast to symbolic methods (e.g. Grobner bases) which manipulate polynomials, numerical algorithms manipulate points on varieties. In this sense, numerical algebraic geometry may be thought of as the geometric side of computational algebraic geometry. In this talk, I will explain the basics ideas underlying the theory of numerical algebraic geometry. 
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Transformation Groups Seminar
Transformation Groups Seminar Speaker: Tao Gong (Western) "Integral cohomologies of classifying spaces of KacMoody groups" Time: 09:30  11:00 Room: MC 107 In this seminar, I will introduce the KacMoody group associated with a Cartan matrix, then how to construct the homotopy colimit of classifying spaces of parabolic subgroups directly. Theoretically, we can know the classifying space of a KacMoody group from the previous homotopy colimit. I will apply that method to detailed computation of integral cohomologies of those classifying spaces with cases of exceptional Lie groups and projective unitary groups, in which spectral sequences are widely used. 







Colloquium
Colloquium Speaker: Yakov ShlapentokhRothman (Univesity of Toronto) "SelfSimilarity and Naked Singularities for the Einstein Vacuum Equations" Time: 15:30  16:30 Room: MC107 We will start with an introduction to the weak cosmic censorship conjecture and the problem of constructing naked singularities for the Einstein vacuum equations. Then we will explain our discovery of a new type of selfsimilarity, and explain how this allows us to construct the desired naked singularity solutions. 



Geometry and Combinatorics
Geometry and Combinatorics Speaker: Matt Larson (Stanford University) "TBA" Time: 15:30  16:30 Room: Zoom 

Transformation Groups Seminar
Transformation Groups Seminar Speaker: Anton Ayzenberg (HSE Moscow) "TBA" Time: 09:30  10:30 Room: MC 107 online talk 






Transformation Groups Seminar
Transformation Groups Seminar Speaker: Grigory Solomadin (HSE Moscow) "TBA" Time: 09:30  10:30 Room: MC 107 online talk 
Colloquium
Colloquium Speaker: Rajesh Pereira (University of Guelph) "TBD" Time: 14:30  15:30 Room: Zoom (details TBD) TBD 
Geometry and matrix analysis
Geometry and matrix analysis Speaker: Rukmini Dey (International Centre for Theoretical Sciences, Bengaluru) "TBA" Time: 09:00  10:00 Room: zoom 








