we classify reflection groups in riemannian manifolds with non negative sectional curvature. this is a joint work with karsten grove.

nonlinear constrained optimization problem can be effectively solved by
minimizing a sequence of unconstrained or linearly constrained
subproblems, where the augmented lagrangian function plays a vital role.
this talk introduces a generalized hestenes-powell augmented lagrangian
function, which can be seen as a continuum of many well-known methods as
specific cases. a new primal dual sequential quadratic programming (pdsqp)
method will be given for minimizing the given augmented lagrangian

the symmetric function operator, nabla, introduced by bergeron and garsia (1999), has many astounding combinatorial properties. the (recently proven) shuffle conjecture of haglund, haiman, loehr, remmel, and ulyanov (2005) relates nabla en to parking functions. the rational compositional shuffle conjecture of the author, bergeron, garsia, and xin (2015) relates a whole family of operators (closely linked to nabla) to rational parking functions. in (2007), loehr and warrington conjectured a relationship between nabla pn and preference functions. we prove this conjecture and provide another combinatorial interpretation in terms of parking functions. this new formula reveals a connection between nabla pn and an operator appearing in the rational compositional shuffle conjecture at $t = 1/q$.

the gaussian distribution---which may be the center of a majority of statistical applications and research---will be introduced. we will focus on an interesting phenomenon on the maximum of a sequence of gaussian variables, and a direct application to human genome research will be displayed.

in 2008, oded schramm asked the following question: for what values of k and q does there exist a stationary, k-dependent sequence of random variables with values in {1,2,...,q} assigning different values to consecutive integers? schramm proved a number of results related to this question, and speculated about what the answer might be in general. as it turns out, the truth is quite different from his informed guess. this is joint work with a. e. holroyd.

given a graph, perform the following randomized coloring procedure to it: pick an edge at random and with probability $p$ color the end vertices of that edge blue; otherwise color them red. repeat indefinitely, choosing the edges with replacement. this induces a random walk in the space of all red/blue colorings of the graph, which converges to a stationary distribution. in this talk we will study this stationary distribution for the complete graph with the goal of getting jay a phd.

calcium is critical to a wide range of physiological processes, including neurological function, immune responses, and muscle contraction. calcium-dependent signaling pathways enlist a variety of proteins and channels that must rapidly and selectively bind calcium against thousand-fold higher cationic concentrations. frequently these pathways further require the co-localization of these proteins within specialized subcellular structures to function properly. our lab has developed multi-scale simulation tools to elucidate how protein structure and co-localization facilitate intracellular calcium signaling. developments include combining molecular simulations with a statistical mechanical model of ion binding, a homogenization theory to upscale molecular interactions into micron-scale diffusion models, and reaction-diffusion simulations that leverage sub-micron microscopy data. in this seminar, i will describe these tools and their applications toward molecular mechanisms of calcium-selective recognition and cross-talk between co-localized calcium binding proteins inside the cell.

schreieder recently introduced a class of smooth projective varieties that have unexpected hodge numbers. we investigate the geometry of these varieties and show how, in dimension two, these varieties may in fact be realized as elliptic modular surfaces.

semitoric integrable systems, or semitoric manifiolds, have been completely classified in terms of five symplectic invariants, but there are properties of these systems which, while encoded in the invariants, are not easy to extract. in this talk i introduce a new invariant of semitoric systems which we call a semitoric helix and i outline its constrction. using this invariant we are able to see clearly the effect of a semitoric blowdown/blowup on the system. we are then able to completely classify minimal semitoric manifolds; those that do not admit a semitoric blowdown. this work is joint with alvaro pelayo and daniel m. kane.