# MSCS Seminar Calendar

Tuesday August 23, 2016

**Model Theory Seminar**

Elimination of Imaginaries in Algebraically Closed Valued Fields (Organizational Meeting)

None (UIC)

11:00 AM in SEO 427

We will begin this semester reading Will Johnson's proof of Haskell-Hrushovski-Macpherso's theorem on elimination of imaginaries in Algebraically Closed Fields
http://arxiv.org/pdf/1406.3654.pdf

**Quantum Topology / Hopf Algebra Seminar**

A Penrose Coloring Formula for Non-planar Graphs

Louis H. Kauffman (UIC)

3:00 PM in SEO 612

Roger Penrose, in his paper "Applications of Negative Dimenionsal Tensors" gave a recursive formula that counts the
number of proper edge-colorings of cubic plane graphs. In this talk we explain how to generalize his method to non-planar
graphs and to generalize the evaluation to a polynomial associated with the graph. This talk will be self-contained.

Wednesday August 24, 2016

Thursday August 25, 2016

**Quantum Topology / Hopf Algebra Seminar**

Quantum walks on Cayley graphs: free quantum field theory derived from simple algorithmic principles.

Giacomo Mauro D'Ariano (Dipartimento di Fisica, via Bassi 6, I-27100 Pavia, Italy)

3:00 PM in SEO 612

Last year I reviewed the derivation of quantum theory of abstract systems from informational theoretical principles. This year I will show how relativistic quantum field theory (QFT) can be derived from additional information-theoretic axioms. The information-theoretic paradigm has the special power of allowing an axiomatization of physics without physical primitives in the axioms (including any mechanical notion, space-time, special relativity, etc.) allowing for a thorough logically coherent foundation toward the solution of the VI Hilbert problem, and with the potential of solving the clash between our current major theories: general relativity (GR) and QFT.
The derivation of QFT starts from simply considering countably many quantum systems in interaction, with the requirements of locality, homogeneity, and isotropy of the interactions. This corresponds to a theory of quantum cellular automata on a Cayley graph of a group G. The restriction to linearity of the evolution leads to a quantum-walk theory. The further restriction to quasi-isometric embedding of the graph in Euclidean space (corresponding to virtually Abelian G) in the limit of “small" wave-vectors (so-called relativistic limit) gives Weyl, Lorentz, and Maxwell QFT in Euclidean space. Relaxing linearity one could extend the derivation to interacting QFT, whereas relaxing Abelianity of G would correspond to QFT in curved space. The theory is purely mathematical, and as such is adimensional, yet it contains the standards for mass, space, and time through the nonlinearities intrinsic to the theory—i.e. maximum wave-vector, a maximum frequency, and a maximum mass (the latter following from unitarity). The relativistic limit connects these standards to the speed of light and the Planck constant, whereas at the maximum value for the particle mass the dispersion relation becomes flat, with interpretation as a mini-black hole, thus setting the scale at Planck’s (therefore “small" wave-vector means much smaller than Planck). All the three standards are in principle measurable with current technology (e.g. the Fermi telescope) from a weak dispersion of vacuum which affects the arrival time of deep-space ultra-high energy cosmic rays. Interestingly the photon comes out as a pair of entangled Fermions, similarly to the de Broglie neutrino theory of radiation, however, Fermionic saturation effects are not visible with current laser technology.
How Einstein relativity principle is restated without using space-time? The inertial reference frames are just the “representations” of the quantum algorithm that leave its “eigenvalue equation” invariant, whereas the invariance itself is the restatement of the relativity principle. The inherent discreteness of the algorithmic description leads to distortions of the Lorentz transformations that would be visible at huge energies. However, the usual special relativity is perfectly recovered at energies even much higher than those ever tested, e.g. those of the observed ultra-high energy cosmic rays. In addition to allowing the theory to provide its own physical standards for space, time, and mass, the discreteness of the theory introduces new phenomenology predicted by GR, e.g. a maximum value for the particle mass, and De Sitter invariance.
Very recently the interacting theory has been addressed, starting with the one-dimensional case which satisfies the locality axiom, corresponding to an Hubbard Fermionic automaton which is analytically solved by the Bethe ansatz. I will show some numerical evaluations of the free and the interacting walk/automaton theories, along with exact path-sum evaluation of the propagator and a simple asymptotic analytical approach that allows to derive a general dispersive Schroedinger equation holding in all regimes for narrow-band states describing quantum particles. Follow-ups and next planned researches about the interacting theory will be discussed at the end of the talk, along with the presentation of a list of open problems.
Main References:
G. M. D’Ariano, G. Chiribella, and P. Perinotti, Quantum Theory from First Principles (Cambridge University Press 2016) [in press]
G. M. D'Ariano, P. Perinotti, Derivation of the Dirac Equation from Principles of Information processing, Phys. Rev. A 90 062106 (2014)
A. Bisio, G. M. D'Ariano, P. Perinotti, Quantum Cellular Automaton Theory of Light, Ann. Phys. 368 177 (2016)
G. M. D'Ariano, N. Mosco, P. Perinotti, A. Tosini, Discrete Feynman propagator for the Weyl quantum walk in 2+1 dimensions EPL 109 40012 (2015)
G. M. D'Ariano, Quantum-Informational Principles for Physics, in A. Aguirre et al. (eds.), Questioning the Foundations of Physics, The Frontiers Collection (Springer 2015)
A. Bisio, G. M. D'Ariano, A. Tosini, Quantum Field as a Quantum Cellular Automaton: the Dirac free evolution in one dimension, Annals of Physics 354 244 (2015)
Giacomo Mauro D'Ariano
Professor of Theoretical Physics
Quantum Foundations
and Quantum Information
Dipartimento di Fisica,
via Bassi 6, I-27100 Pavia, Italy
email:dariano@unipv.it
tel:+39 0382 987 484
fax:+39 0382 987 793
mobile:+39 347 0329998
skype: giacomo_mauro_dariano
AIM: dariano13
WEBSITES:
www.qubit.it
www.quantummechanics.it
www.quantumoptics.it
www.meccanicaquantistica.it
www.otticaquantistica.it

Friday August 26, 2016

**Homotopy Theory Seminar**

On the cohomology of the classifying spaces of projective unitary groups

Xing Gu (UIC)

12:30 PM in SEO 1227

Let $\mathbf{B}PU(n), \mathbf{B}U(n)$, and $K(\mathbb{Z},3)$ denote
respectively the projective unitary group of rank $n$, the unitary group of
rank $n$, and the Eilenberg-Maclane space with the third homotopy group
being $\mathbb{Z}$. We construct a cohomological Serre spectral sequence
$E_{*}^{*,*}$ with $E_{2}^{s,t}\simeq H^{s}(K(\mathbb{Z},3),
H^{t}(\mathbf{B}U(n)))$ and converging to $H^{*}(\mathbf{B}PU(n))$.
Moreover we determine all of its differentials. This enables us to
calculate $H^{*}(\mathbf{B}PU(n))$ up to extension.

**Geometry, Topology and Dynamics Seminar**

Random Grids in G-spaces

Jayadev S. Athreya (University of Washington)

3:00 PM in SEO 636

We show how to define a general notion of a random grid, how it generalizes the notion of random Euclidean lattices and random affine lattices, and describe how it gives a natural notion of a random hyperbolic lattice. This is joint work with Gregory Margulis and Yair Minsky.

We will be going for a seminar dinner. Email schapos@uic.edu if you'd like to join.

**Analysis and Applied Mathematics Seminar**

The 2D Boussinesq equations with fractional dissipation

Jiahong Wu (Oklahoma State)

4:00 PM in SEO 636

The Boussinesq equations concerned here model geophysical flows such as atmospheric fronts and ocean circulations. In addition, they play an important role in the study of Rayleigh-Benard convection. Mathematically the 2D Boussinesq equations serve as a lower-dimensional model of the 3D hydrodynamics equations. The global regularity problem on the 2D Boussinesq equations with partial or fractional dissipation has attracted considerable attention in the last few years. This talk presents some recent work on the 2D Boussinesq equations with general critical dissipation as well as the global regularity result on the 2D Boussinesq equations with vertical dissipation. If time permits, we will also briefly discuss the regularity problem on the partially dissipated Boussinesq equations in a bounded domain.

Tuesday August 30, 2016

**Model Theory Seminar**

Algebrically Closed Valued Fields

Dave Marker (UIC)

11:00 AM in SEO 427

We will begin our series of lectures on elimination of imaginaries in algebraically closed valued fields (ACVF)
with a brief introduction to valued field and some of the results that are needed to prove quantifier elimination.
A good reference is van den Dries

*Lectures on the Model Theory of Valued Fields*http://www.math.uiuc.edu/~vddries/Wednesday August 31, 2016

**Algebraic Geometry Seminar**

Fundamental Groups of F-regular Singularities via F-Signature

Kevin Tucker (UIC)

4:00 PM in SEO 427

The F-signature is a numerical invariant of singularities which measures the asymptotic number of splittings of iterates of Frobenius. The positivity of the F-signature characterizes F-regular singularities, which are closely related to KLT singularities in characteristic zero. After giving an overview, I will discuss new transformation rules for F-signature under finite maps. These transformation rules allow us to show finiteness of the etale local fundamental group for F-regular singularities, analogous to results of Xu and Greb-Kebekus-Peternell for KLT singularities in characteristic zero. This is joint work with Javier Cravajal-Rojas and Karl Schwede.

**Statistics Seminar**

COMPETING BROWNIAN PARTICLES

Andrey Sarantsev (University of California, Santa Barbara)

4:00 PM in SEO 636

Consider a finite or infinite system of Brownian particles on the real line. Each particle moves as a Brownian motion
with drift and diffusion coefficients depending on its current rank relative to other particles. These systems were
introduced in Banner, Fernholz, Karatzas (2005). Since then, extensive theory was developed for finite systems.
However, infinite systems proved to be much more difficult. We survey the latest results.

TBA

Monday September 12, 2016

**Analysis and Applied Mathematics Seminar**

Inverse Random Source Scattering Problems

Peijun Li (Purdue)

4:00 PM in SEO 636

This talk concerns the source scattering problems for acoustic wave propagation, which is governed by the two- or three-dimensional stochastic Helmholtz equation. As a source, the electric current density is assumed to be a random function driven by an additive colored noise. Given the random source, the direct problem is to determine the radiated random wave field. The inverse problem is to reconstruct statistical properties of the source from the boundary measurement of the radiated random wave field. In this work, we consider both the direct and inverse problems. We show that the direct problem has a unique mild solution via a constructive proof. Using the mild solution, we derive effective Fredholm integral equations for the inverse problem. A regularized Kaczmarz method is developed by adopting multi-frequency scattering data to overcome the challenges of solving the ill-posed and large scale integral equations. Numerical experiments will be shown to demonstrate the efficiency of the proposed method. The framework and methodology developed here are expected to be applicable to a wide range of stochastic inverse source problems.

Wednesday September 14, 2016

**Statistics Seminar**

New Approaches to Fast Approximate Bayesian Nonparametric Inference

George Karabatsos (UIC)

4:00 PM in SEO 636

Dirichlet process (DP) mixture models, as well as models
with mixture distribution assigned a general Bayesian nonparametric (BNP)
prior distribution on the space of probability measures, are
widely-applied and flexible models that can provide reliable statistical
inferences complex data. For such Bayesian mixture models, in practice,
posterior inferences are usually conducted using MCMC, which however, is
prohibitively slow for large data sets. Also for such models, prior
specification can be non-trivial in practice. As alternatives to MCMC, I
consider two new approaches to fast and approximate BNP inference for
large data sets. First, I show that if the ordinary least-squares (OLS)
estimator of the linear regression coefficients is specified as a
functional of the DP posterior distribution, then this functional has
posterior mean given by an observation-weighted ridge regression
estimator, with ridge (coefficient shrinkage) parameter given by the DP
precision parameter;
and has a heteroscedastic-consistent posterior covariance matrix.
This result is based on the multivariate delta method applied to
prior-informed bootstrap distribution approximation to the DP posterior.
Second, I consider an approximation to the BNP (infinite) mixture model
that I introduced and studied in several articles, defined by ordinal
regression mixture weights.The approximate model is defined by a (large)
finite mixture, with each component distribution multiplied by a histogram
bin indicator function. I show that posterior inference with this
approximate BNP model can be conducted by iteratively-reweighted least
squares estimation for the mixture weight parameters, and least-squares
estimation for the component densities, all involving computations that
are orders of magnitude faster that MCMC-based inference of the original
mixture model. This is also true for a version of the approximate model
that is defined by an ordinal regression of DPs. I illustrate the two
approximate BNP methods through the analysis of real data sets.

TBA

Friday September 16, 2016

**Departmental Colloquium**

Heat Rises: 100 Years of Rayleigh-Bénard Convection

Charles Doering (University of Michigan)

3:00 PM in SEO 636

Buoyancy forces result from density variations, often due to temperature variations, in the presence of gravity.
Buoyancy-driven fluid flows shape the weather, ocean and atmosphere dynamics, the climate, and the structure
of the earth and stars. In 1916 Lord Rayleigh published a paper entitled "On Convection Currents in a Horizontal
Layer of Fluid, when the Higher Temperature is on the Under Side" introducing the minimal mathematical model
of buoyancy-driven fluid flow now known as Rayleigh-Bénard convection. For a century this model has served
as a primary paradigm of complex nonlinear dynamics displaying spontaneous symmetry breaking and pattern
formation, chaos and turbulence. Here we describe progress and challenges for the analysis of Rayleigh's
model in the strongly nonlinear regime of turbulent convection.

Tea and light refreshments after the talk in SEO 300.

Monday September 19, 2016

Friday September 23, 2016

Monday September 26, 2016

Wednesday September 28, 2016

**Statistics Seminar**

Some Recent Developments on the Applications of Evolutionary Algorithm in the Statistical Optimization

Frederick Phoa (Academia Sinica, Taiwan R.O.C.)

4:00 PM in SEO 636

Nature-inspired metaheuristic methods, like the particle swarm optimization and many others, enjoys fast convergence towards optimal solution via a series of inter- particle communication. Such methods are common for the optimization problem in engineering, but few in statistics problem. It is especially difficult to implement in some fields of statistics as the search spaces are mostly discrete, while most natural heuristic methods require continuous search domains. This talk introduces a new method called the Swarm Intelligence Based (SIB) method for optimization in statistics problems, featuring the searches within discrete space. Such fields include experimental designs, community detection, change-point analysis, variable selection, etc. The SIB method is a nature-inspired metaheuristic method that includes several operations. This method is advantageous over the traditional particle swarm optimization and many other heuristic approaches in the sense that it is ready for the search of both continuous and discrete domains, and its global best particle is guaranteed to monotonically move towards the optimum. The SIB method is demonstrated in several examples. Several extensions from the standard framework are also discussed at the end of this talk.

Monday October 3, 2016

Wednesday October 5, 2016

**Algebraic Geometry Seminar**

Rational Curves on Complete Intersections in Positive Characteristic

Matthew Woolf (UIC)

4:00 PM in SEO 427

In this talk, I will discuss joint work with Eric Reidl showing that a general Calabi-Yau or general type complete intersection over a field of positive characteristic is not uniruled. I will also discuss applications of this work to deducing bounds on the dimension of complete intersections containing too many rational curves.

Monday October 10, 2016

Wednesday October 12, 2016

Friday October 14, 2016

Monday October 24, 2016

Wednesday October 26, 2016

Monday October 31, 2016

Friday November 4, 2016

Monday November 7, 2016

Monday November 14, 2016