Department of Mathematics
Mathematics Colloquium
Organizer Mailing list: https://groups.google.com/forum/#!forum/ccnymathcolloquium/joinThe Mathematics Department Colloquium typically meets on Thursdays from 12:30 pm to 1:20 pm in NAC 6/114. This will typically be preceded by tea and coffee at noon in the math lounge, and will be followed by lunch. To receive announcements via email, please join our google group
Upcoming talks

Thursday, November 08, 2018, 12:30PM, NAC 6/114
Yotam Smilansky (The Hebrew University of Jerusalem), Multiscale substitution schemes and Kakutani sequences of partitions.Substitution schemes provide a classical method for constructing tilings of Euclidean space. Allowing multiple scales in the scheme, we introduce a rich family of sequences of tile partitions generated by the substitution rule, which include the sequence of partitions of the unit interval considered by Kakutani as a special case. In this talk we will use new path counting results for directed weighted graphs to show that such sequences of partitions are uniformly distributed, thus extending Kakutani's original result. Furthermore, we will describe certain limiting frequencies associated with sequences of partitions, which relate to the distribution of tiles of a given type and the volume they occupy.

Thursday, November 29, 2018, 12:30PM, NAC 6/114
Philippe Sosoe (Cornell U.), TBATBA
Most recent talks

Thursday, October 18, 2018, 12:30PM, NAC 6/114
Claire Burrin (Rutgers University), Windings of closed geodesicsFor closed curves in the plane, the winding number is famously a homotopy invariant, but will not distinguish two curves that, say, differ by a nullhomotopic loop. However, in the case of regular curves, the winding number is also a regular homotopy invariant. For a (cusped) hyperbolic hyperbolic surface equipped with a nonvanishing vector field, there is an analogous invariant. We examine growth, distribution, and density results for the number of 'prime' geodesics of fixed winding. This is based on joint work with Flemming von Essen.

Thursday, October 11, 2018, 12:30PM, NAC 6/114
Raquel Perales (Instituto de Matemáticas, UNAM), Maximal Volume Entropy Rigidity for $RCD^*((N1),N)$ (Joint work with Connell, Dai, NunezZimbron, SuarezSerrato, Wei)For $n$dimensional Riemannian manifolds $M$ with Ricci curvature bounded below by $(n1)$, the volume entropy is bounded above by $n1$. If $M$ is compact, it is known that the equality holds if and only if $M$ is hyperbolic. We show the same maximal entropy rigidity result holds for a class of metric measure spaces known as $RCD^*(K,N$ spaces. While the upper bound follows quickly, the rigidity case is quite involved due to the lack of a smooth structure on these spaces.

Thursday, September 13, 2018, 12:30PM, NAC 6/114
Tobias Johnson (College of Staten Island (CUNY)), The frog model on treesImagine that every vertex of a graph contains a sleeping frog. At time 0, the frog at one vertex wakes up and begins a random walk. When it moves to a new vertex, the sleeping frog there wakes up and begins its own random walk, which in turn wakes up any sleeping frogs it lands on, and so on. This process is called the frog model, and despite the cutesy name, it's a serious object of study for which many basic questions remain open.
I'll talk about the frog model on trees, where the model displays some interesting phase transitions. In particular, I'll (mostly) answer a question posed by Serguei Popov in 2003 by showing that on a binary tree, all frogs wake up with probability one, while on a 5ary or higher tree, some frogs remain asleep forever with probability one. This is joint work with Christopher Hoffman and Matthew Junge.