Director of Institute for Pure & Applied Mathematics, UCLA, Los Angeles

Mon 3 Feb 2014, 3:00pm
Institute of Applied Mathematics
LSK 460

From PDEs to Information Science and Back (IAMPIMS Distinguished Colloquium)

LSK 460
Mon 3 Feb 2014, 3:00pm4:00pm
Abstract
The arrival of massive amounts of data from imaging, sensors, computation and the internet brought with it significant challenges for information science. New methods for analysis and manipulation of big data have come from many scientific disciplines. The first focus of this presentation is the application of ideas from PDEs, such as variational principles and numerical diffusion, to image and data analysis. Examples include denoising, segmentation, inpainting and texture extraction for images. The second focus is the development of new ideas in information science, such as wavelets, softthresholding, sparsity and compressed sensing. The subsequent application of these ideas to PDEs and numerical computation is the third focus of this talk. Examples include wavelet analysis for turbulent flows, the use of softthresholding in computation of PDEs with multiscale features, and the construction of “compressed modes” (modes that are compactly supported in space) for density functional theory and other PDEs that come from variational principles.
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ESB 4127

Mon 3 Feb 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127

The Higher Chow Groups of GLn

ESB 4127
Mon 3 Feb 2014, 3:00pm4:00pm
Abstract
If X is a variety over a field, the Chow groups of X are defined in terms of closed subvarieties of X and form a kind of cohomology theory for X. Higher Chow groups, defined by Spencer Bloch in the 1980s in terms of subvarieties on X x A^m and now related to the theory of motivic cohomology, extend the theory of Chow groups, and may be nonzero even when the ordinary Chow groups vanish. I will explain how the higher Chow groups of GLn are related to a 'suspension' of the ordinary Chow groups of projective space. Time permitting, I will conjecture how this relationship might extend to 'suspensions' of the Chow groups of Grassmanians.
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UBC

Tue 4 Feb 2014, 2:00pm
Mathematical Education
Math 126

Academic Motivation in Calculus

Math 126
Tue 4 Feb 2014, 2:00pm3:00pm
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Basque Center for Applied Mathematics

Tue 4 Feb 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Flow control in the presence of shocks

ESB 2012
Tue 4 Feb 2014, 3:30pm4:30pm
Abstract
In this talk we present some joint work in collaboration with C. Castro (UPM, Madrid), R. Lecaros (CMM Chile) and F. Palacios (Stanford) on flow control.
We address a classical optimal control problem of inverse design, aiming to identify the initial source leading to a desired final configuration.
First, in the onedimensional case, we explain why classical strategies, based on linearization methods, fail, because of the lack of regularity of solutions. We then introduce an alternating descent method that exploits the generalized gradients that take into account the sensitivity of the smooth arcs of the solutions but also of shock locations.
We compare the performance of the method with classical purely discrete strategies through various numerical experiments.
We also address the multidimensional case and point towards perspectives of future development.
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Basque Center for Applied Mathematics

Wed 5 Feb 2014, 3:00pm
Department Colloquium
ESB 2012 (PIMS)

Optimal placement of sensors and actuators for waves

ESB 2012 (PIMS)
Wed 5 Feb 2014, 3:00pm4:00pm
Abstract
In this lecture we address the problem of the optimal placement of sensors and actuators for wave propagation problems.
Using Fourier series representation the problem can be recast as a spectral optimal design problem, involving all the spectrum of the Laplacian.
We show that, depending on the complexity of the data to be observed/controlled, several scenarios have to be distinguished. Those in which the solution is a classical set constituted by a finite number of simply connected subdomains, others in which the optimal set is of Cantor type and those leading to relaxation phenomena.
We also explain how closely this topic is related to the fine properties of the high frequency behavior of the eignefunctions of the Laplacian which is intimately linked to the ergodicity properties of the dynamical system generated by the corresponding billiard.
We shall also discuss the same problem for heat processes showing that, in that frame, according to intuition, the problem is governed by a finite number of Fourier modes.
These results will be illustrated by numerical simulations.
The lecture is conceived for a general audience and unnecessary technicalities will be avoided. It is based on recent joint work in collaboration with Y. Privat and E. Trélat from UMPC, Paris.
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UAlberta

Wed 5 Feb 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)

pcurvature and modular forms

ESB 4127 (host: UBC)
Wed 5 Feb 2014, 3:00pm4:00pm
Abstract
(Vectorvalued) modular forms appear all over string theory. Often, one wants to know whether the Fourier coefficients are integers, or if it is already known they must be integral, one would like to know consequences. In my talk I'll describe the most effective tool for these sorts of questions: pcurvature.
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University of Washington

Wed 5 Feb 2014, 4:00pm
Probability Seminar
ESB 2012

Systems of reflected diffusions with annihilations through membranes

ESB 2012
Wed 5 Feb 2014, 4:00pm5:00pm
Abstract
We study interacting particle systems which can model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition. The hydrodynamic limit and the fluctuation limit for the particle densities can be described, respectively, by a coupled Partial Differential Equation (PDE) and a Gaussian process solving a Stochastic Partial Differential Equation (SPDE). New tools of discrete approximations to reflected diffusions will be discussed. (Joint work with ZhenQing Chen)
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Technion  Israel Institute of Technology

Wed 5 Feb 2014, 4:00pm
SPECIAL
Topology and related seminars
ESB 4133

The curve complex and 3manifolds

ESB 4133
Wed 5 Feb 2014, 4:00pm5:00pm
Abstract
The curve complex is a finite dimensional, locally infinite, unbounded and 17hyperbolic simplicial
complex associated with surfaces. The intricate relationship between the curve complex of surfaces
embedded in 3manifolds and the topology and geometry of the manifolds will be discussed in the talk.
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PhD Student, Mechanical Engineering Department, UBC

Wed 5 Feb 2014, 4:00pm
Fluids Lab Meeting
LSK 203

Design, Simulation and Construction Feasibility Study of Light Scattering Optical Particle Counter (OPC)

LSK 203
Wed 5 Feb 2014, 4:00pm5:00pm
Abstract
Aerosols as a colloidal system of solid or liquid particles in a gas are significant twophase systems which have an important rule in environmental, biological, health, industrial and other scientific studies. According to these important rules, some instruments namely “Aerosol Spectrometer” have been developed to measure aerosols’ characteristics and specifically size distribution of the sample particles. Optical Particle Counters (OPCs) are one of these instruments which are able to count and measure the particles’ size distribution in a specific aerosol sample. In the current study, an optical particle counter has been designed mechanically and optically. To validate our design, both optical and mechanical operation of the design was simulated. In this case the Mie theory was used for optical simulation and prescription of the scattered light by particles and the optical parts were redesigned using geometrical optic principals and simulations’ results to achieve an optimum sketch. Fluid flow was simulated by ANSYS Fluent and particles were tracked by means of a particle tracking UDF code in Lagrangian approach. Since the difference in particles’ refractive indices can cause wrong measured size, a novel method based on measurement of scattered light in different angular intervals was presented. This new method was checked by Mie theory simulation and its functionality was investigated. At last, a new sizing method by calculating intensity of collected light in CMOS sensors was studied experimentally under highly controlled conditions. This study showed that there is a good agreement between Mie theory and experimental study results for particles with bigger than 15 micron diameter.
Farzad received his undergraduate degree in Mechanical Engineering from BuAli Sina University, (Iran), 2010. Then, in 2013, he graduated with MSc degree in Mechanical Engineering (Thermofluids) from Sharif University of Technology. He started his PhD career in UBC in January 2014 under supervision of Prof. Gwynn Elfring.
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UBC

Tue 11 Feb 2014, 2:00pm
Mathematical Education
Math 126

A history of the American Mathematics Curriculum

Math 126
Tue 11 Feb 2014, 2:00pm3:00pm
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UBC

Wed 12 Feb 2014, 3:00pm
Probability Seminar
ESB 2012

Logarithmic corrections to scaling for the 4 dimensional weakly selfavoiding walk: watermelon networks

ESB 2012
Wed 12 Feb 2014, 3:00pm4:00pm
Abstract
We calculate the logarithmic correction to the decay of the critical twopoint function for networks of p mutuallyavoiding weakly selfavoiding walks joining two distant points on the 4dimensional integer lattice. While similar results have been obtained previously for dimensions d > 4 by lace expansion, our proof is based on a rigorous renormalisation group analysis of a representation of the selfavoiding walk as a supersymmetric field theory.
The talk is based on joint and ongoing work with Roland Bauerschmidt, David Brydges and my supervisor Gordon Slade.
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University of Texas at Austin.

Wed 12 Feb 2014, 3:15pm
Topology and related seminars
ESB 4133

Masur criterion analog for OUT(F) and applications

ESB 4133
Wed 12 Feb 2014, 3:15pm4:15pm
Abstract
The Masur criterion for Teichmuller geodesics relates the geometry of the Teichmuller space and random walks on the mapping class group of a surface to dynamical properties of vertical foliations of quadratic differentials. A major problem in the study of outer automorphism group OUT(F) of a nonabelian free group has been to find an analog for the Masur criterion. We discuss difficulties and explain our approach to this problem. We also mention applications of this result particularly in describing the space of random walks on the group of OUT(F). This is joint work with Alexandra Pettet and Patrick Reynolds.
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IAM, UBC

Thu 13 Feb 2014, 12:30pm
Graduate Student Seminar
Math 204

Stochastic differential equations and \alpha stable noise processes

Math 204
Thu 13 Feb 2014, 12:30pm1:30pm
Abstract
In this talk, I'll introduce some basics of stochastic differential equations, used for modelling dynamical systems that are subject to stochastic effects. Typically, stochastic differential equations have a Gaussian white noise term that introduces the randomness into the dynamics for the purposes of capturing processes that are difficult (or undesirable) to quantify.
After this, I will discuss including a stochastic forcing known as \alpha stable noise into the dynamics. This noise process is used for incorporating stochastic effects with infinite variance into dynamical systems, however obtaining analytical results is significantly more challenging since moments of \alpha stable distributions do not exist beyond first order (in general). I will give some results from my stochastic averaging research project and try to offer some interesting questions to attendees.
This talk should be moderately accessible and will be on Beamer slides
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UBC

Thu 13 Feb 2014, 12:30pm
Lunch Series on Teaching & Learning
Math 126

Lunch Series: The Math Exam Educational Resource Wiki

Math 126
Thu 13 Feb 2014, 12:30pm2:00pm
Abstract
In this talk, we will discuss the Math Educational Resource Wiki. Formerly called the Math Exam Resource, this wiki, located at http://wiki.ubc.ca/Science:Math_Education_Resources which redirects to http://wiki.ubc.ca/Science:Math_Exam_Resources has evolved into much more than just an exam solution database. We will first briefly demonstrate the wiki, then present usage statistics, recent enhancements, future ideas as well as advantages and limitations of the wiki platform. We will also discuss ways to supplement your current teaching with material from the wiki and where you, as an instructor, would like to see this resource go. We will also consider how this wiki can be enhanced to further facilitate teaching first year calculus courses.
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University of Toronto

Thu 13 Feb 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 4133 at PIMS

Big frequency cascades in the nonlinear Schrödinger evolution

ESB 4133 at PIMS
Thu 13 Feb 2014, 3:30pm4:30pm
Abstract
I will outline a construction of an exotic solution of the nonlinear Schrödinger equation that exhibits a big frequency cascade. Recent advances related to this construction and some open questions will be surveyed.
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University of Toronto

Fri 14 Feb 2014, 3:00pm
Department Colloquium
MATX 1100

Hamiltonian Partial Differential Equations

MATX 1100
Fri 14 Feb 2014, 3:00pm4:00pm
Abstract
Ideas from harmonic analysis and dynamical systems have led to spectacular advances in the understanding of Hamiltonian partial differential equations. This colloquium will survey some of these developments and highlight issues at the research frontier.
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Department of Aerospace & Mechanical Engineering and Mathematics, Viterbi School of Engineering, University of Southern California

Mon 24 Feb 2014, 3:00pm
Institute of Applied Mathematics
LSK 460

Random Walks, Markov Chains, and Cancer Metastasis Models (IAMPIMS Distinguished Colloquium)

LSK 460
Mon 24 Feb 2014, 3:00pm4:00pm
Abstract
The talk will describe a recent mathematical/computational model for understanding aspects of cancer metastasis, initiated when primary tumor cells enter the vasculature and lymphatic system becoming circulating tumor cells (CTC's). The model is based on a Markov chain dynamical system designed so that the transition matrix has as it's steadystate a `target' vector obtained from an autopsy data set. The target vector, chosen for a given type of primary cancer (i.e. lung), contains the distribution of metastatic tumors from an ensemble population. The transition matrix can be associated with a metastatic network (directed graph) with disease progression modeled as a random walker on the network. We focus on primary lung cancer, and using the metastatic network obtained from the transition matrix, we quantify (probabilistically) the most probable disease progression pathways, along with mean firstpassage times of progression.
We highlight the multidirectional nature of the progression pathways that the model produces (selfseeding and reseeding) which supports recent experimental observations carried out at Memorial SloanKettering Cancer Center on the importance of primary tumor selfseeding. We also will describe how we use the concept of metastatic entropy to compare the complexity of different cancer types. The work is sponsored by the National Cancer Institute under the auspices of The Scripps Research Institute Physical Sciences Oncology Center `The Physics and Mathematics of Cancer Metastasis'. If time permits, we will finish with a brief overview of related projects modeling the fluid phase of cancer.
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Department of Mathematics, Boise State University

Tue 25 Feb 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133

Statistical Tests for Regularization in Illposed Inverse Problems

ESB 4133
Tue 25 Feb 2014, 12:30pm2:00pm
Abstract
Most inverse problems are illposed due to the fact that inputs such as parameters, physics and data are missing or inconsistent. This results in solution estimates that are not unique or unstable, i.e. small changes in the inputs result in large changes in the estimates. One common approach to resolving illposedness is to use regularization methods whereby information is added to the problem so that data are not overfitted. Alternatively, one could take the Bayesian point of view and assign a probability distribution to the unknowns and estimate it by exploiting Monte Carlo techniques.
In this work we take the regularization approach and use uncertainties to weight added information and data in an optimization problem. This allows us to apply statistical tests with the null hypothesis that inputs are combined within their uncertainty ranges to produce estimates of the unknowns. For example, the Discrepancy Principle can be viewed as using a chisquared test to determine the regularization parameter.
The chisquared method developed by myself and colleagues uses a chisquared test similar to the Discrepancy Principle, but differs in that the test is applied to the regularized residual rather than the data residual. This approach leads to a general methodology of using statistical tests to estimate regularization parameters or uncertainties in an inversion. I will give statistical tests for nonlinear algorithms and show results from benchmark problems in Geophysics. I will also describe how statistical tests can be used to find a regularization parameter for Total Variation and show results from Imaging.
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Oregon State University

Tue 25 Feb 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

How to lift positive Ricci curvature

ESB 2012
Tue 25 Feb 2014, 3:30pm4:30pm
Abstract
We show how to lift positive Ricci and almost nonnegative curvatures from an orbit space M/G to the corresponding Gmanifold, M. We apply the results to get new examples of Riemannian manifolds that satisfy both curvature conditions simultaneously. This is joint work with Fred Wilhelm.
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York University

Tue 25 Feb 2014, 4:00pm
Discrete Math Seminar
ESB 4133

Schur analogues in noncommutative symmetric functions

ESB 4133
Tue 25 Feb 2014, 4:00pm5:00pm
Abstract
The noncommutative symmetric functions and quasisymmetric functions
are the second and third examples of a combinatorial Hopf algebra that
one encounters (the first being the symmetric functions). In recent
years there have been at least two bases proposed as an analogues of
the Schur functions and they are in addition to the
"ribbon=funadmantal^*" basis. I'll list properties that we would want
these bases to have as analogues of the Schur functions and then
explain some computational results that tell us what is possible
(surprisingly, it is not possible to have it all!). I will also
discuss some symmetric function positivity open problems that we hope
these bases will resolve.
This is joint work with Laura Colmenarejo.
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Charles University in Prague

Wed 26 Feb 2014, 11:00am
PIMS Seminars and PDF Colloquiums
ESB 4133

Symplectic Geometry Seminar: On the Poisson geometry of symplectic quotients.

ESB 4133
Wed 26 Feb 2014, 11:00am12:00pm
Abstract
Given a finite dimensional unitary representation of a compact Lie group G one constructs the socalled symplectic quotient.This is given by the space of Gorbits in the zero fibre of the moment map. The symplectic quotient is stratified by symplectic manifolds and can be understood as a semialgebraic set. We will present results related to the isomorphism problem of symplectic quotients. In particular, we will be concerned with the question when a symplectic quotient is symplectomorphic to a finite unitary quotient.
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Columbia

Wed 26 Feb 2014, 1:30pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)

Instability in algebraic geometry

ESB 4127 (host: UBC)
Wed 26 Feb 2014, 1:30pm2:30pm
Abstract
In order to construct moduli spaces in algebraic geometry, one typically must specify a notion of semistability for the objects one wishes to parameterize. To the objects that are omitted, the unstable objects, one can often associate a real number which measures "how unstable" that object is. In fact we can think of the moduli stack of all objects as stratified by locally closed substacks corresponding to objects of varying degrees of instability. The key examples of this phenomenon are the KempfNess stratification of the unstable locus in GIT and the Shatz stratification of the moduli of Gbundles on a smooth projective curve. I will discuss a framework for describing stability conditions and stratifications of an arbitrary algebraic stack which provide a common generalization of these examples. Time permitting, I will discuss how some commonly studied moduli problems, such as the moduli of Kstable varieties and the moduli of Bridgelandsemistable complexes on a smooth projective variety, fit into this framework. One key construction assigns to any point in an algebraic stack a potentially large topological space parameterizing all possible `isotrivial degenerations' of that point. When the stack is BG for a reductive G, this recovers the spherical building of G, and when the stack is X/T for a toric variety X, this recovers the support of the fan of X.
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ETH Zurich

Wed 26 Feb 2014, 3:00pm
Probability Seminar
ESB 2012

Large deviations and disconnection for random interlacements

ESB 2012
Wed 26 Feb 2014, 3:00pm4:00pm
Abstract
In this talk I will describe results obtained in two recent articles in collaboration with Xinyi Li concerning large deviations for the occupationtime profile in a large box of Z^d, d≥3, for random interlacements at a given level, and the probability that random interlacements disconnect a macroscopic body from infinity, when the vacant set is in the percolative regime.
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UAlberta

Wed 26 Feb 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)

An introduction to the GrossSiebert program (Part I)

ESB 4127 (host: UAlberta)
Wed 26 Feb 2014, 3:00pm4:00pm
Abstract
I will attempt to give an overview of the GrossSiebert program, emphasizing its guiding principles and their connection to the StromingerYauZaslow conjecture.
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Georgia Institute of Technology

Wed 26 Feb 2014, 3:15pm
Topology and related seminars
ESB 4133

Towards a motivic simplicial EHP spectral sequence

ESB 4133
Wed 26 Feb 2014, 3:15pm4:15pm
Abstract
This talk will discuss a version in A^1 homotopy theory of the classical EHP sequence of James and Toda using the simplicial suspension map. This is joint work in progress with Ben Williams.
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UBC

Thu 27 Feb 2014, 3:30pm
Number Theory Seminar
room MATH 126

The dynamical MordellLang problem

room MATH 126
Thu 27 Feb 2014, 3:30pm4:30pm
Abstract
Let X be a Noetherian space, let f be a continuous selfmap on X, let Y be a closed subset of X, and let x be a point in X. We show that the set containing all positive integers n such that the nth iterate of x under f lands in Y is a union of at most finitely many arithmetic progressions along with a set of Banach density 0. This is joint work with Jason Bell and Tom Tucker.
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UBC

Thu 27 Feb 2014, 4:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102

The hardcore model: Phase transition and computational complexity of counting (I)

Math Annex 1102
Thu 27 Feb 2014, 4:00pm5:30pm
Abstract
This is the first in a series of talks on the papers:
(1) D. Weitz, Counting independent sets up to the tree threshold,
STOC'06, 2006
(2) A. Sly, Computational transition at the uniqueness threshold,
FOCS'10, 2010
Both papers study the hardcore model, a model for a lattice gas.
The hardcore model on a graph G=(V,E) is a probability measure on
the independent sets of G, that is, the subsets I of V with
the property that no two vertices of I are neighbours. The
probability of an independent set I is proportional to
lambda^I, where lambda is a positive parameter. The
problem of interest is computing the partition function Z of the
model, that is, the sum of lambda^I over all choices of I.
In the Computer Science literature, this is known as the problem of
counting (weighted) independent sets. Since this is wellknown to be
computationally hard, one allows for algorithms that
compute Z only approximately, and also restrict attention to
graphs with degree bounded by a constant d. The combined results
of (1) and (2) show that there is a phase transition for the
computational hardness of this problem: Z can be approximated in
polynomial time (with respect to the size of G) if and only if
lambda is below a threshold lambda_c(d). Moreover, lambda_c
is also a threshold value for a Statistical Mechanical phase
transition, namely it separates the regimes of uniqueness and
nonuniqueness of Gibbs measures for the hardcore model on
dregular trees. In this first, introductory talk, we will explain
the model, briefly survey the literature and cover the
prerequisites concerning the hardcore model on trees.
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Charles University, Prague

Fri 28 Feb 2014, 3:00pm
Department Colloquium
ESB 2012 (PIMS)

Sparse  Dense Phenomena (PIMS/UBC Distinguished Colloquium)

ESB 2012 (PIMS)
Fri 28 Feb 2014, 3:00pm4:00pm
Abstract
The dichotomy between sparse and dense structures is one of the profound, yet fuzzy, features of contemporary mathematics and computer science.
We present a framework for this phenomenon, which equivalently defines sparsity and density of structures in many different yet equivalent forms, including effective decomposition properties. This has several applications to model theory, algorithm design and, more recently, to structural limits.
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Note for Attendees
Refreshments start 15 minutes before the talk in the IAM Lounge, Room 306 of the LSK building.