## Seminars and Colloquia by Series

Friday, November 16, 2018 - 15:55 , Location: Skiles 006 , , University of Michigan , , Organizer: Galyna Livshyts
TBANote the special time!
Friday, November 16, 2018 - 11:00 , Location: Skiles 006 , , University of Michigan , , Organizer: Galyna Livshyts
TBA
Wednesday, October 24, 2018 - 13:55 , Location: Skiles 006 , , Kent State University , , Organizer: Galyna Livshyts
TBA
Wednesday, October 24, 2018 - 12:55 , Location: Skiles 006 , , Kent State University , , Organizer: Galyna Livshyts
TBA
Wednesday, October 10, 2018 - 12:55 , Location: Skiles 006 , Josiah Park , Georgia institute of Technology , , Organizer: Galyna Livshyts
It has been known that when an equiangular tight frame (ETF) of size |Φ|=N exists, Φ ⊂ Fd (real or complex), for p > 2 the p-frame potential ∑i ≠ j | < φj, φk > |p achieves its minimum value on an ETF over all N sized collections of vectors. We are interested in minimizing a related quantity: 1/ N2 ∑i, j=1 | < φj, φk > |p . In particular we ask when there exists a configuration of vectors for which this quantity is minimized over all sized subsets of the real or complex sphere of a fixed dimension. Also of interest is the structure of minimizers over all unit vector subsets of Fd of size N. We shall present some results for p in (2, 4) along with numerical results and conjectures. Portions of this talk are based on recent work of D. Bilyk, A. Glazyrin, R. Matzke, and O. Vlasiuk.
Wednesday, October 3, 2018 - 13:55 , Location: Skiles 005 , Allysa Genschaw , University of Missouri , , Organizer: Michael Lacey
Wednesday, September 19, 2018 - 13:55 , Location: Skiles 005 , Marcin Bownik , University of Oregon , Organizer: Shahaf Nitzan
Thursday, September 6, 2018 - 15:05 , Location: Skiles 006 , , ETH Zurich , Organizer: Mayya Zhilova
Thursday, August 30, 2018 - 15:05 , Location: Skiles 006 , , University of North Carolina, Chapel Hill , Organizer: Mayya Zhilova
Monday, August 20, 2018 - 15:05 , Location: Skiles 005 , Esther Ezra , Georgia Tech , Organizer: Prasad Tetali
A recent extension by Guth (2015) of the basic polynomial partitioning technique of Guth and Katz (2015) shows the existence of a partitioning polynomial for a given set of k-dimensional varieties in R^d, such that its zero set subdivides space into open cells, each meeting only a small fraction of the given varieties.  For k > 0, it is unknown how to obtain an explicit representation of such a partitioning polynomial and how to construct it efficiently.  This, in particular, applies to the setting of n algebraic curves, or, in fact, just lines, in 3-space.  In this work we present an efficient algorithmic construction for this setting almost matching the bounds of Guth (2015); For any D > 0, we efficiently construct a decomposition of space into O(D^3\log^3{D}) open cells, each of which meets at most O(n/D^2) curves from the input.  The construction time is O(n^2), where the constant of proportionality depends on the maximum degree of the polynomials defining the input curves.  For the case of lines in 3-space we present an improved implementation using a range search machinery. As a main application, we revisit the problem of eliminating depth cycles among non-vertical pairwise disjoint triangles in 3-space, recently been studied by Aronov et al.  Joint work with Boris Aronov and Josh Zahl.