Seminars and Colloquia by Series

Field Theoretical Interpretation of QM Wave Functions and Quantum Mechanism of High Tc Superconductivity

Series
PDE Seminar
Time
Tuesday, March 5, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Professor Shouhong Wang – Indiana University –

First, we introduce a new field theoretical interpretation of quantum mechanical wave functions, by postulating that the wave function is the common wave function for all particles in the same class determined by the external potential V, of the modulus of the wave function represents the distribution density of the particles, and the gradient of phase of the wave function provides the velocity field of the particles. Second, we show that the key for condensation of bosonic particles is that their interaction is sufficiently weak to ensure that a large collection of boson particles are in a state governed by the same condensation wave function field under the same bounding potential V. For superconductivity, the formation of superconductivity comes down to conditions for the formation of electron-pairs, and for the electron-pairs to share a common wave function. Thanks to the recently developed PID interaction potential of electrons and the average-energy level formula of temperature, these conditions for superconductivity are explicitly derived. Furthermore, we obtain both microscopic and macroscopic formulas for the critical temperature. Third, we derive the field and topological phase transition equations for condensates, and make connections to the quantum phase transition, as a topological phase transition. This is joint work with Tian Ma.

The nu+ equivalence class of genus one knots

Series
Geometry Topology Seminar
Time
Monday, March 4, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 154
Speaker
Kouki Sato – University of Tokyo
The nu+ equivalence is an equivalence relation on the knot concordance group. It is known that the equivalence can be seen as a certain stable equivalence on knot Floer complexes, and many concordance invariants derived from Heegaard Floer theory are invariant under the equivalence. In this talk, we show that any genus one knot is nu+ equivalent to one of the unknot, the trefoil and its mirror.

Chow rings of matroids, ring of matroid quotients, and beyond

Series
Algebra Seminar
Time
Monday, March 4, 2019 - 12:50 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Chris Eur – University of California, Berkeley –
We introduce a certain nef generating set for the Chow ring of the wonderful compactification of a hyperplane arrangement complement. This presentation yields a monomial basis of the Chow ring that admits a geometric and combinatorial interpretation with several applications. Geometrically, one can recover Poincare duality, compute the volume polynomial, and identify a portion of a polyhedral boundary of the nef cone. Combinatorially, one can generalize Postnikov's result on volumes of generalized permutohedra, prove Mason's conjecture on the log-concavity of independent sets for certain matroids, and define a new valuative invariant of a matroid that measures its closeness to uniform matroids. This is an on-going joint work with Connor Simpson and Spencer Backman.

A partial order on nu+ equivalence classes

Series
Geometry Topology Seminar Pre-talk
Time
Monday, March 4, 2019 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 257
Speaker
Kouki Sato – University of Tokyo
I will review the definition of nu+ equivalence, which is an equivalence relation on the knot concordance group, and introduce a partial order on the equivalence classes. This partial order is preserved by all satellite maps and some concordance invariants. We also consider full-twist operations and its relationship to the partial order.

Local Guarantees in Graph Cuts and Clustering

Series
ACO Student Seminar
Time
Friday, March 1, 2019 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Roy Schwartz – CS, Technion –

Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Minimum s-t Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization.

Here, we are given a graph with edges labeled + or - and the goal is to produce a clustering that agrees with the labels as much as possible: + edges within clusters and - edges across clusters.

The classical approach towards Correlation Clustering (and other graph cut problems) is to optimize a global objective, e.g., minimizing the total number of disagreements or maximizing the total number of agreements.

We depart from this and study local objectives: minimizing the maximum number of disagreements for edges incident on a single node, and the analogous max min agreements objective.

This naturally gives rise to a family of basic min-max graph cut problems.

A prototypical representative is Min-Max s-t Cut: find an s-t cut minimizing the largest number of cut edges incident on any node.

In this talk we will give a short introduction of Correlation Clustering and discuss the following results:

  1. an O(\sqrt{n})-approximation for the problem of minimizing the maximum total weight of disagreement edges incident on any node (thus providing the first known approximation for the above family of min-max graph cut problems)
  2. a remarkably simple 7-approximation for minimizing local disagreements in complete graphs (improving upon the previous best known approximation of 48)
  3. a (1/(2+epsilon))-approximation for maximizing the minimum total weight of agreement edges incident on any node, hence improving upon the (1/(4+epsilon))-approximation that follows from the study of approximate pure Nash equilibria in cut and party affiliation games.

Joint work with Moses Charikar and Neha Gupta.

Joint distribution of Busemann functions for the corner growth model

Series
Stochastics Seminar
Time
Thursday, February 28, 2019 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Wai Tong (Louis) Fan – Indiana University, Bloomington –
We present the joint distribution of the Busemann functions, in all directions of growth, of the exactly solvable corner growth model (CGM). This gives a natural coupling of all stationary CGMs and leads to new results about geodesics. Properties of this joint distribution are accessed by identifying it as the unique invariant distribution of a multiclass last passage percolation model. This is joint work with Timo Seppäläinen.

Estimates for multilinear Schur multipliers

Series
High Dimensional Seminar
Time
Wednesday, February 27, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anna Skripka – University of New mexico –

Linear Schur multipliers, which act on matrices by entrywisemultiplications, as well as their generalizations have been studiedfor over a century and successfully applied in perturbation theory (asdemonstrated in the previous talk). In this talk, we will discussestimates for finite dimensional multilinear Schur multipliersunderlying these applications.

Schur multipliers in perturbation theory

Series
Analysis Seminar
Time
Wednesday, February 27, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Anna Skripka – University of New Mexico
Linear Schur multipliers, which act on matrices by entrywisemultiplications, as well as their generalizations have been studiedfor over a century and successfully applied in perturbation theory. Inthis talk, we will discuss extensions of Schur multipliers tomultilinear infinite dimensional transformations and then look intoapplications of the latter to approximation of operator functions.

Braid groups

Series
Research Horizons Seminar
Time
Wednesday, February 27, 2019 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dan Margalit – Georgia Tech
An element of the braid group can be visualized as a collection of n strings that are braided (like a hair braid). Braid groups are ubiquitous in mathematics in science, as they record the motions of a number of points in the plane. These points can be autonomous vehicles, particles in a 2-dimensional medium, or roots of a polynomial. We will give an introduction to and a survey of braid groups, and discuss what is known about homomorphisms between braid groups.

Inference of evolutionary dynamics of heterogeneous cancer and viral populations

Series
Mathematical Biology Seminar
Time
Wednesday, February 27, 2019 - 11:01 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Pavel Skums – GSU/CDC –

Inference of evolutionary dynamics of heterogeneous cancer and viral populations Abstract: Genetic diversity of cancer cell populations and intra-host viral populations is one of the major factors influencing disease progression and treatment outcome. However, evolutionary dynamics of such populations remain poorly understood. Quantification of selection is a key step to understanding evolutionary mechanisms driving cancer and viral diseases. We will introduce a mathematical model and an algorithmic framework for inference of fitness landscapes of heterogeneous populations from genomic data. It is based on a maximal likelihood approach, whose objective is to estimate a vector of clone/strain fitnesses which better fits the observed tumor phylogeny, observed population structure and the dynamical system describing evolution of the population as a branching process. We will discuss our approach to solve the problem by transforming the original continuous maximum likelihood problem into a discrete optimization problem, which could be considered as a variant of scheduling problem with precedent constraints and with non-linear cumulative cost function.

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