Wednesday 3-4, Location JMH 404

- From Grand Central Terminal: Buy one round trip, off peak ticket to Fordham. Take any train stopping at Fordham (after 9 a.m. these are at 25/55 after the hour). Upon arrival at the Fordham stop, walk east on Fordham Road to Bathgate Avenue and turn left onto Bathgate. You will come to a campus gate. Enter and turn right at the first road. Pass Walsh Hall. The next building is Mulcahy (JMH). The math department offices are on the 4th floor.
- From the A train/D train line: Take the A to 145th St and transfer to the D train. Take the D train to Fordham Road. Walk east on Fordham Road to Bathgate Avenue and turn left onto Bathgate. You will come to a campus gate. Enter and turn right at the first road. Pass Walsh Hall. The next building is Mulcahy (JMH). The math department offices are on the 4th floor.

**Peter Fu - Fordham University** - September 27

- Title: One-Particle-Thick Coarse-Grained Lipid Bilayer Membrane Simulations in LAMMPS
Abstract: Lipid bilayer membranes have been extensively studied by coarse-grained molecular dynamics simulations. Numerical efficiencies have been reported in the cases of aggressive coarse-graining, where several lipids are coarse-grained into a particle of size 4 - 6 nm so that there is only one particle in the thickness direction. Yuan et al. proposed a pair-potential between these one-particle-thick coarse-grained lipid particles to capture the mechanical properties of a lipid bilayer membrane, such as gel-fluid-gas phase transitions of lipids, diffusion, and bending rigidity. In this work we implement such an interaction potential in LAMMPS to simulate large-scale lipid systems such as a giant unilamellar vesicle (GUV) and red blood cells (RBCs). We also consider the effect of cytoskeleton on the lipid membrane dynamics as a model for RBC dynamics, and incorporate coarse-grained water molecules to account for hydrodynamic interactions. The interaction between the coarse-grained water molecules (explicit solvent molecules) is modeled as a Lennard-Jones (L-J) potential. To demonstrate that the proposed methods do capture the observed dynamics of vesicles and RBCs, we focus on two sets of LAMMPS simulations: 1. Vesicle shape transitions with enclosed volume; 2. RBC shape transitions with different enclosed volume.

**Chika Mese - Johns Hopkins University** - October 11

- Title: Harmonic maps in rigidity problems
Abstract: When can a geometric structure be deformed and when is it rigid? One of the main applications of the theory of harmonic map is in answering this question. In this talk, we explain how harmonic maps are used to prove some rigidity theorems. In particular, we will discuss my joint work G. Daskalopoulos on the holomorphic rigidity of Teichmuller space.

**Brian Freidin - Brown University **- October 18

- Title: Geometry of harmonic maps into singular spaces
Abstract: Harmonic map theory for singular targets was first introduced in the '90s by Gromov and Schoen to prove p-adic superrigidity. We will describe briefly how harmonic maps into metric spaces are defined, and then how the geometry of metric spaces of curvature bounded above influences the behavior of harmonic maps. In particular, we will describe several Liouville-type theorems about the constancy of harmonic maps.

**Hengyu Zhou - Sun-Yat-Sen University **- October 25

- Title: Nonparametric Mean Curvature type motion of graphs with Prescribed Angle Conditions
Abstract: In this talk we consider a class of nonparametric mean curvature motions of graphs in $M\times R$ over a bounded smooth domain with prescribed contact angle conditions. Their long time existence and uniform convergence will be demonstrated. One application is Capillary problem with prescribed contact angle in Riemannian manifolds. We also give an example that similar results are not true in the case of warped product manifolds.

**Theodora Bourni - University of Tennessee **- November 1

- Title: Ancient Pancakes
Abstract: We construct a compact, convex ancient solution of mean curvature flow in $\R^{n+1}$ with $O(1)\times O(n)$ symmetry that lies in a slab of width $\pi$. We provide detailed asymptotics for this solution and show that, up to rigid motions, it is the only compact, convex, $O(n)$-invariant ancient solution that lies in a slab of width $\pi$ and in no smaller slab. This work is joint with Mat Langford and Giuseppe Tinaglia.

**Otis Chodosh - Princeton University **- November 8

- Title: Minimal surfaces in 3-manifolds: existence and rigidity results.
Abstract: Minimal surfaces in 3-manifolds are natural generalizations of geodesics on surfaces. I'll discuss some existence (joint with D. Ketover) and rigidity (joint with M. Eichmair) results for such surfaces, emphasizing this analogy.