This talk is focused on recent developments within the field of topoly optimization, e.g. optimal material distribution. The main focus concerns the current state-of-the-art, which is that large structural systems has until now been dealing mainly with the design of individual parts - and not with complete assemblies or structures. In this talk ...

Creator:

Aage, Niels (Technical University of Denmark)

Created:

2016-06-08

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Wave propagation in optical lattices with honeycomb background, termed Photonic Graphene, is investigated. A tight binding approximation leads to a coupled mode system. In bulk media a nonlinear Dirac type system is obtained which describes conical, elliptical and straight-line diffraction. With rapidly varying helical waveguides linear and nonl...

Creator:

Ablowitz, Mark J. (University of Colorado)

Created:

2016-10-31

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

There is a long story of the role nonlinearity plays in optics and photonics. From the early experiments in second harmonic generation to the demonstration of optical solitons in fiber optics, the field continues to evolve in several directions. Rather than presenting well developed ideas, in this seminar I will attempt to provide examples mostl...

Mean field type models describing the limiting behavior of stochastic differential game problems as the number of players tends to infinity, have been recently introduced by J-M. Lasry and P-L. Lions. They may lead to systems of evolutive partial differential equations coupling a forward Bellman equation and a backward Fokker-Planck equation. Th...

Creator:

Achdou, Yves (Université de Paris VII (Denis Diderot))

Created:

2012-11-12

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

At the heart of every local search procedure is a directed graph on candidate solutions (states) such that every unsatisfying state has at least one outgoing arc. In randomized local search the hope is that a random walk on the graph reaches a satisfying state (sink) quickly. We give a general algorithmic local lemma by establishing a sufficient...

Creator:

Achlioptas, Dimitris (University of California, Santa Cruz)

Created:

2015-05-22

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Moderator: Ming Hu, University of Toronto Yoni Acriche (eBay), Jakub Marecek (IBM), Ramesh Johari (Stanford University), Karan Girotra (INSEAD), David Shmoys (Cornell University)

Creator:

Acriche, Yoni (eBay); Girotra, Karan (INSEAD); Hu, Ming (Moderator, University of Toronto); Johari, Ramesh (Stanford University); Marecek, Jakub (IBM Research Division); Shmoys, David B. (Cornell University)

Created:

2017-07-25

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

I will discuss results by R. Latala concerning tail behaviour of multivariate polynomials in independent Gaussian variables and show how when combined withclassical functional inequalities they give estimates for polynomials and more generally smooth functions with bounded derivatives of higher order for a more general class of non-necessarily p...

Creator:

Adamczak, Radoslaw (University of Warsaw)

Created:

2012-06-26

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The Gromov-Hausdorff distance between two metric spaces is an important tool in geometry, but it is difficult to compute. For example, the Gromov-Hausdorff distance between unit spheres of different dimensions is unknown in nearly all cases. I will introduce recent work by Lim, Mémoli, and Smith that finds the exact Gromov-Hausdorff distances be...

Creator:

Adams, Henry (Colorado State University)

Created:

2022-08-04

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Suppose ball-shaped sensors wander in a bounded domain. A sensor doesn't know its location but does know when it overlaps a nearby sensor. We say that an evasion path exists in this sensor network if a moving intruder can avoid detection. Vin de Silva and Robert Ghrist give a necessary condition, depending only on the time-varying connectivity d...

Creator:

Adams, Henry (University of Minnesota, Twin Cities)

Created:

2014-03-05

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Consider a Vietoris-Rips complex of the circle with the geodesic metric. This simplicial complex has an infinite number of vertices, one for each point in the circle. A theorem of Jean-Claude Hausmann implies that for small connectivity parameter, the Vietoris-Rips complex is homotopy equivalent to a circle. What happens as the connectivity para...

Creator:

Adams, Henry (University of Minnesota, Twin Cities)

Created:

2014-05-06

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Consider the Vietoris-Rips complex for n evenly-spaced points around a circle. For small choices of the connectivity parameter, this complex is homotopy equivalent to a circle. For n even and for a connectivity parameter slightly less than the diameter of the circle, this complex is the boundary of a cross-polytope and is homeomorphic to the (n/...

Creator:

Adams, Henry (University of Minnesota, Twin Cities)

Created:

2013-10-01

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The theory and practice of topological data analysis (TDA) over the past decade has been dominated by the notion and application of persistent homology. Given a representation of the persistent homology of a filtered structure, it is easy to compute the Euler characteristic curve (ECC) which gives the value of the Euler characteristic of the str...

Creator:

Adler, Robert

Created:

2013-10-11

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

My first working assumption for this tutorial will be that the participants know something about persistent homology (PH). In particular, they know that PH is associated with filtrations, the two most common being the filtrations of upper or lower level sets of smooth functions and filtrations arising from building simplicial (Rips, Cech) comple...

Creator:

Adler, Robert (Technion-Israel Institute of Technology)

Created:

2013-10-03

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

We revisit the theory by Eggers [Phys. Rev. Lett., vol. 93, pp 094502, 2004] of the critical capillary number forthe Landau-Levich-Derjaguin forced dewetting transition. We generalize this prediction to large contact angles and arbitrary viscosity ratios and express the critical capillary number as a function of the imposed contact angle in the ...

Creator:

Afkhami, Shahriar (New Jersey Institute of Technology)

Created:

2018-03-26

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The contextual bandit problem is a classic example of the statistical tradeoff between exploration and exploitation. Upon taking an action, a learner only observes the reward of that action, while no feedback on the other possible actions is received. In additional to the natural information tradeoff between experimenting with unknown actions an...

Creator:

Agarwal, Alekh (Microsoft Research)

Created:

2016-05-16

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.