Fiber bundles with fiber a surface arise in many areas including hyperbolic geometry, symplectic geometry, and algebraic geometry. Up to isomorphism, a surface bundle is completely determined by its monodromy representation, which is a homomorphism to a mapping class group. This allows one to use algebra to study the topology of surface bundles. Unfortunately, the monodromy representation is typically difficult to 'compute' (e.g. determine its image). In this talk, I will discuss some recent work toward computing monodromy groups for holomorphic surface bundles, including certain examples of Atiyah and Kodaira. This can be applied to the problem of counting the number of ways that certain 4-manifolds fiber
over a surface. This is joint work with Nick Salter.

Geometric integrator for classic mechanics has provided fruitful results. In this talk, we consider
generalizations to three special settings. One is stiff system which comes from semi-discretization of Hamilton PDE,
traditional exponential integrators are modified to preserve Poisson structure and energy; one is for Lie group,
where configuration space is Lie group, group structure of space is considered to construct variational integrator, in contrast to
constrained mechanics; the final is Control system, we take into account nonobservability analysis of control system, which appears as invariance of special group actions, Kalman Filter is modified based on decomposition of space. Such reduced Filter attains state of
art result.

The Ricci iteration is a discrete analogue of the Ricci flow. Introduced in 2007, it has been studied extensively on Kähler manifolds, providing a new approach to uniformisation. In the talk, we will define the Ricci iteration on compact homogeneous spaces and discuss a number of existence, convergence and relative compactness results. This is largely based on joint work with Timothy Buttsworth (Queensland), Yanir Rubinstein (Maryland) and Wolfgang Ziller (Penn).

Complex biological systems involve multiple space and time scales. To get an integrated understanding of these systems involves multiscale modeling, computation and analysis. In this talk, I will discuss two such examples in cell biology and illustrate how to use multiscale methods to explain experimental data. The first example is on chemotaxis of bacterial populations. I will present recent progress on embedding information of single cell dynamics into models of cell population dynamics. I will clarify the scope of validity of the well-known Keller-Segel chemotaxis equation and discuss alternative models when it breaks down. The second example is on the axonal cytoskeleton dynamics in health and disease. I will present a stochastic multiscale model that gave the first mechanistic explanation for the cytoskeleton segregation phenomena observed in many neurodegenerative diseases.

I will present a recent proof of the Multiplicity One Conjecture in Min-max theory. This conjecture was raised by Marques and Neves. It says that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves are all two-sided and have multiplicity one. As direct corollaries, it implies the generalized Yau's conjecture for such manifolds with positive Ricci curvature, which says that there exist infinitely many pairwise non-isometric minimal hypersurfaces, and the Weighted Morse Index Bound Conjecture by Marques and Neves.

This talk concerns singular values of M-fold products of i.i.d. right-unitarily invariant N x N random matrix ensembles. As N tends to infinity, the height function of the Lyapunov exponents converges to a deterministic limit by work of Voiculescu and Nica-Speicher for M fixed and by work of Newman and Isopi-Newman for M tending to infinity with N. In this talk, I will show for a variety of ensembles that fluctuations of these height functions about their mean converge to explicit Gaussian fields which are log-correlated for M fixed and have a white noise component for M tending to infinity with N. These ensembles include rectangular Ginibre matrices, truncated Haar-random unitary matrices, and right-unitarily invariant matrices with fixed singular values. I will sketch our technique, which derives a central limit theorem for global fluctuations via certain conditions on the multivariate Bessel generating function, a Laplace-transform-like object associated to the spectral measures of these matrix products. This is joint work with Vadim Gorin.

I will describe joint work with Jared Wunsch on propagation of
singularities for some semiclassical Schrodinger equations where the
potential has singularities normal to an interface. Semiclassical
singularities of a given strength propagate across the interface, but only
up to a threshold. This is due to diffracted singularities which are
weaker than the incident singularity by a factor depending on the
regularity of the potential. Time permitting, I will give applications to
logarithmic resonance-free regions in scattering theory.

Cathy Pearl is a UC San Diego alumnae and current Head of Conversation Design Outreach at Google. She earned her degrees in Cognitive Science from UC San Diego, and a Computer Science master's from Indiana University. She is the author of the 2016 book, 'Designing Voice User Interfaces,' published by O'Reilly Media and has worked with many innovators in the voice-recognition sphere including Nuance. Her broad background makes her a popular speaker, having done some rocket science, as a software designer for NASA, integrating voice recognition for banks, airlines and healthcare. She's also known for her degital expertise on love and romance, writing a Love Data blog focused on 'data-driven love in our modern world' - even performing analysis of the use of Twitter in dating.

Classically, general Markov processes were studied through their relationship to operator semigroups. The analytic challenges of operator semigroup theory helped motivate the development of alternative approaches including stochastic equations as introduced by Ito and martingale problems as introduced by Stroock and Varadhan. These approaches have dominated work on Markov processes in the mathematics literature while the Kolmogorov forward equation that characterizes the one dimensional distributions of the process receives much more attention in the physics literature (cf. Fokker-Planck equation, master equation). The talk will include a brief over view of all these approaches paying particular attention to the equivalence of the different approaches in characterizing Markov processes.

Recent developments in numerical optimization show that the augmented Lagrangian method (ALM) is very effective in solving large scale convex semidefinite programming. Due to the possible lack of primal-dual-type error bounds, it was not clear whether the Karush–Kuhn–Tucker (KKT) residuals of the sequence generated by the ALM for solving convex semidefinite programming converge superlinearly. We resolve this issue by establishing the R-superlinear convergence of the KKT residuals generated by the ALM under only a mild dual-type error bound condition, for which neither the primal nor the dual solution is required to be unique.