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CMSA MATHEMATICAL PHYSICS SEMINAR: Baohua Fu
Chinese Academy of Science
Equivariant compactifications of vector groups
on Monday, April 23, 2018, at 12:00 - 1:00 PM in CMSA Building, 20 garden St., G02
In 1954, Hirzebruch raised the problem to classify smooth compactifications of vector spaces with second Betti number 1, which is known till now up to dim 3. In 1999, Hassett-Tschinkel considered the equivariant version of this problem and obtained the classification up to dim. 3. I'll report recent progress on this (equivariant) problem. In particular, we obtain the classification up to dimension 5.

DIFFERENTIAL GEOMETRY SEMINAR: Jiaping Wang
Minnesota
Structure at infinity for four dimensional shrinking Ricci Solitons
on Tuesday, April 24, 2018, at 4:15 PM in Science Center 507
Ricci solitons, as self-similar solutions to the Ricci flows, play a prominent role in the study of singularity formation of Ricci flows. In this talk, we are primarily concerned with four dimensional shrinking Ricci solitons and discuss joint work with Ovidiu Munteanu on their geometric structure at infinity.

LOGIC SEMINAR: Paul Baginski
Fairfield University
Model Theoretic Advances for Groups With Bounded Chains of Centralizers
on Tuesday, April 24, 2018, at 5:15 PM in Science Center 507
A group G has bounded chains of centralizers (G is \M_C) if every chain of centralizers C_G(A_1) \leq C_G(A_2) \leq ... is finite. While this class of groups is interesting in its own right, within model theory MC groups have been examined because they strictly contain the class of stable groups. Stable groups robustly extend ideas from algebraic groups, such as dimension and independence, to a wider setting, including free groups. Stable groups gain much of their strength through a chain condition known as the Baldwin-Saxl chain condition, which implies the \M_C property as a special case. Several basic, but key, properties of stable groups have been observed by Wagner [4] and others to follow purely from the \M_C condition (this builds upon the work of Bludov [2], Khukhro [3], and others). These properties were, as one would expect, purely group-theoretic. From the perspective of logic, the class of \M_C groups should be unruly, since the MC condition is not first-order (unless one insists on a uniform bound to the lengths of the chains). Yet the speaker and Tuna Altınel [1] have uncovered that MC groups possess a logical property of stable groups as well, namely the abundance of definable nilpotent subgroups. We shall present this result and describe the current investigations for finding an analogue for solvable subgroups. (Joint work with Tuna Altınel, Universit´e Lyon 1) References [1] T. Altınel and P. Baginski, Definable envelopes of nilpotent subgroups of groups with chain conditions on centralizers, Proc. Amer. Math. Soc. 142 (2014), no. 5, 1497–1506. [2] V.V. Bludov, On locally nilpotent groups with the minimality condition for centralizers, Algebra Logika 37 (1998), 270–278. [3] E.I. Khukhro, On solubility of groups with bounded centralizer chains, Glasg. Math. J. 51 (2009), 49–54. [4] F.O. Wagner, Stable Groups, London Mathematical Society Lecture Note Series, 240. Cambridge University Press, 1997.

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM : Xi Yin
Harvard University
How we can learn what we want to know about M-theory
on Wednesday, April 25, 2018, at 4:30 PM in CMSA Building, 20 Garden St, G10
M-theory is a quantum theory of gravity that admits an eleven dimensional Minkowskian vacuum with super-Poincare symmetry and no dimensionless coupling constant. I will review what was known about M-theory based on its relation to superstring theories, then comment on a number of open questions, and discuss how they can be addressed from holographic dualities. I will outline a strategy for extracting the S-matrix of M-theory from correlation functions of dual superconformal field theories, and in particular use it to recover the 11D R^4 coupling of M-theory from ABJM theory.

INFORMAL DYNAMICS & GEOMETRY SEMINAR: Yongquan Zhang
Harvard University
Andreev's theorem on hyperbolic polyhedra and Kleinian reflection groups
on Wednesday, April 25, 2018, at 4:00 pm in Science Center 530
One way to obtain a Kleinian group is to consider the group generated by reflections in the faces of a hyperbolic polyhedron with dihedral angles submultiples of \pi. Andreev’s theorem guarantees the existence of hyperbolic polyhedra with non-obtuse dihedral angles satisfying certain combinatorial conditions. In this talk, I will construct a one dimensional family of hyperbolic polyhedra with the help of Andreev’s theorem so that the Kleinian groups obtained from reflections in some of the faces realize a one dimensional deformation of a convex cocompact acylindrical hyperbolic 3-manifold.

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