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Events happening on October 18, 2016

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Oct. 18, 2016 10am (Math 350)	Geometry/Analysis Mason Thomas Pelfrey (CU Boulder) X Cartan's method of equivalence is a technique for determining when two geometric objects are equivalent up to diffeomorphism by finding invariants of the objects under some group action. A control system is an under determined set of ODEs which show up most often when describing mechanical systems which are "steerable" in some sense. In this talk, we will discuss what it means for two control systems to be equivalent and how Cartan's Method can be used to determine if an equivalence exists between two control systems. Control Systems and Cartan's Method of Equivalence
Oct. 18, 2016 10am (MATH 220)	Number Theory Arseniy Sheydvasser (Yale University) X Studying circle/sphere packings that arise as limit sets of discrete subgroups of the hyperbolic isometric group is a long studied problem, generalizing the familiar case of the Apollonian gasket. Far less is known about integral packings, where the curvature of each sphere is required to be an integer---even producing explicit examples is a non-trivial task. In this talk, I will discuss a new method of explicitly constructing such sphere packings by considering special types of orders in rational quaternion algebras. Quaternion Algebras and Integral Sphere Packings
Oct. 18, 2016 12:10pm (MATH …	Kempner Laurentiu Maxim (University of Wisconsin, Madison) X By analogy with knot theory, complex hypersurfaces can be studied via Alexander-type invariants of their complements. I will discuss old and new results concerning rigidity properties of such invariants, including (twisted) Alexander polynomials, $L2$ -betti numbers and Novikov homology of hypersurface complements. The first part of the talk will be an overview of the subject, addressed to a general audience. In the second part I will show how intersection homology and perverse sheaves can be used to relate the local and global topology of such hypersurface complements. Alexander-type invariants of complex hypersurface complements
Oct. 18, 2016 1pm (MATH 220)	Agnes Szendrei (CU Boulder) Taylor Terms, Part 4: Olsak's Theorem
Oct. 18, 2016 2pm (MATH 350)	Lie Theory JP Cossey (University of Akron) X Let $G$ be a finite group and p a prime. A block of a finite group $G$ is a certain subset of the characters of $G$ that are in a sense related when “reduced modulo $p$ ”. There are certain particularly nice “small” blocks, called the nilpotent blocks of $G$ , but there is no easily checked sufficient condition for a block $B$ to be nilpotent. In this talk we will discuss one proposed sufficient condition, and introduce enough algebraic combinatorics to show that the conjecture holds for the symmetric groups. The conjecture is also known to hold for solvable groups and some other types of blocks of arbitrary finite groups. Small blocks of finite groups Sponsored by the Meyer Fund
Oct. 18, 2016 2pm (MATH 220)	Mark Pullins (CU) Bad groups, 1
Oct. 18, 2016 3pm (MATH 350)	Topology Laurentiu Maxim (U Wisconsin Madison) X By analogy with knot theory, complex hypersurfaces can be studied via Alexander-type invariants of their complements. I will discuss old and new results concerning rigidity properties of such invariants, including (twisted) Alexander polynomials, L2-betti numbers and Novikov homology of hypersurface complements. The first part of the talk will be an overview of the subject, addressed to a general audience. In the second part I will show how intersection homology and perverse sheaves can be used to relate the local and global topology of such hypersurface complements. Alexander-type invariants of complex hypersurface complements
Oct. 18, 2016 4pm (Math 220)	Algebraic Geometry Steffen Marcus (TCNJ) X Logarithmic structures provide geometers a systematic way of picking out, locally, a finite collection of functions and their powers on algebraic varieties. The combinatorial structure of these local choices comes along for the ride. In this talk I will report on work in progress with Alana Huszar, Matthew Satriano, and Martin Ulirsch to develop a couple of ways of altering logarithmic structures to highlight, combinatorially, slightly more of the geometry of the underlying space. I hope to also discuss potential applications to tropical geometry and Gromov-Witten theory. Pointed and twisted logarithmic structures Sponsored by the Meyer Fund

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