### Week of January 28, 2018

 11:00am to 12:30pm - ELH 100 - Differential Geometry SCGAS - (Conference) 25th Southern California Geometric Analysis Seminar Conference website: https://www.math.uci.edu/scgas Please register at the conference website if planning to attend.
 4:00pm to 5:00pm - RH 306 - Special Colloquium Maryann Hohn - (UCSB) Research with Undergraduates - Successes and Pitfalls Undergraduates are curious about research in mathematics: what kinds of questions do mathematicians ask, what does research entail, how do you begin to solve a new problem. In this talk, we will discuss integrating undergraduate research projects inside the classroom and how to expose students to new mathematical questions in both upper and lower division courses. We will then talk more generally about setting students up for success in the classroom.
 3:00pm to 4:00pm - RH 306 - Analysis Weimin Sheng - (Zhejiang University) Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems In this talk, I will introduce our recent work on Gauss curvature flow with Xu-Jia Wang and Qi-Rui Li. In this work we study a contracting flow of closed, convex hypersurfaces in the Euclidean space $\R^{n+1}$ with the speed $f r^{\alpha} K$, where $K$ is the Gauss curvature, $r$ is the distance from the hypersurface to the origin, and $f$ is a positive and smooth function. We prove that if $\alpha\ge n+1$, the flow exists for all time and converges smoothly after normalization to a hypersurface, which is a sphere if $f\equiv 1$.  Our argument provides a new proof for the classical Aleksandrov problem  ($\alpha = n+1$) and resolves the dual q-Minkowski problem introduced by Huang, Lutwak, Yang and Zhang recently, for the case q<0 ($\alpha>n+1$). If $\alpha< n+1$, corresponding to the case q > 0, we also establish the same results for even function f and origin-symmetric initial condition, but for non-symmetric f, counterexample is given for the above smooth convergence. 4:00pm - RH 306 - Differential Geometry Norman Zergaenge - (University of Warwick) Convergence of Riemannian manifolds with scale invariant curvature bounds A key challenge in Riemannian geometry is to find best" metrics on compact manifolds. To construct such metrics explicitly one is interested to know if approximation sequences contain subsequences that converge in some sense to a limit manifold. In this talk we will present convergence results of sequences of closed Riemannian 4-manifolds with almost vanishing L2-norm of a curvature tensor and a non-collapsing bound on the volume of small balls.  For instance we consider a sequence of closed Riemannian 4-manifolds, whose L2-norm of the Riemannian curvature tensor is uniformly bounded from above, and whose L2-norm of the traceless Ricci-tensor tends to zero.  Here, under the assumption of a uniform non-collapsing bound, which is very close to the euclidean situation, and a uniform diameter bound, we show that there exists a subsequence which converges in the Gromov-Hausdor sense to an Einstein manifold. To prove these results, we use Jeffrey Streets' L2-curvature  ow. In particular, we use his tubular averaging technique" in order to prove fine distance estimates of this flow which only depend on significant geometric bounds.
 2:00pm - - Mathematical Physics S. Kocic - (U Mississippi) Renormalization and rigidity of circle diffeomorphisms with breaks Abstract: Renormalization provides a powerful tool to approach universality and rigidity phenomena in dynamical systems. In this talk, I will discuss recent results on renormalization and rigidity theory of circle diffeomorphisms (maps) with a break (a single point where the derivative has a jump discontinuity) and their relation with generalized interval exchange transformations introduced by Marmi, Moussa and Yoccoz. In a joint work with K.Khanin, we proved that renormalizations of any two sufficiently smooth circle maps with a break, with the same irrational rotation number and the same size of the break, approach each other exponentially fast. For almost all (but not all) irrational rotation numbers, this statement implies rigidity of these maps: any two sufficiently smooth such maps, with the same irrational rotation number (in a set of full Lebesgue measure) and the same size of the break, are $C^1$-smoothly conjugate to each other. These results can be viewed as an extension of Herman's theory on the linearization of circle diffeomorphisms.