USC

Wed 23 Jan 2019, 2:45pm
Topology and related seminars
ESB 4133

Fibrant resoultions of motivic Thom spectra

ESB 4133
Wed 23 Jan 2019, 2:45pm3:45pm
Abstract
This is a joint work with G.Garkusha. In the talk I will discuss the construction of fibrant replacements for spectra consisting of Thom spaces (suspension spectra of varieties and algebraic cobordism MGL being the motivating examples) that uses the theory of framed correspondences. As a consequence we get a description of the infinite loop space of MGL in terms of Hilbert schemes.
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Mathematics, UBC

Wed 23 Jan 2019, 2:45pm
Mathematical Biology Seminar
ESB 4127

The dynamics of diffusively coupled oscillators

ESB 4127
Wed 23 Jan 2019, 2:45pm3:45pm
Abstract
When two identical nonlinear oscillators are coupled through a 1D bulk diffusion field, new patterns of synchronization occur that would be absent in the uncoupled system. Furthermore, if the two oscillators are quiescent, the effect of the coupling can be to turn the oscillations on. Mathematically, the models consist of systems of nonlinear ODEs coupled with linear diffusive PDEs. Through a detailed bifurcation analysis of three different examples, we reveal some of the underlying mechanisms behind phenomena as diverse as the diffusion sensing of reacting agents, the synchronization of chaotic oscillations and the formation of membranebound patterns at the cellscale level.
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IST Austria

Wed 23 Jan 2019, 4:00pm
Department Colloquium
MATH 100

Modeling the dynamics of extortion and cooperation in iterated games

MATH 100
Wed 23 Jan 2019, 4:00pm5:00pm
Abstract
Iterated games are the baseline model to explain how cooperation can evolve in repeated interactions. The basic idea is that individuals are more likely to cooperate if they can expect their beneficiaries to remember and to return their cooperative acts in future. However, six years ago, William Press and Freeman Dyson have shown that certain repeated games also allow individuals to employ extortionate strategies. By using an extortionate strategy, players can guarantee that they systematically outperform their opponent, irrespective of the opponent’s reaction. In this talk, I will first present a simple proof for the existence of these extortionate strategies. This proof applies to both, finitely and infinitely repeated games with arbitrarily many players. I will then discuss under which circumstances such strategies can emerge in an evolutionary process, and how successful they are against actual human players. In the end, I will discuss a few interesting generalizations and open problems.
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University of Maryland, College Park

Thu 24 Jan 2019, 2:15pm
MATH 126

Applied Stochastics Seminar: Numerical methods for uncertainty quantification  from noise parameterization to efficient simulation of parameterized stochastic systems

MATH 126
Thu 24 Jan 2019, 2:15pm3:15pm
Details
Abstract:
For a reliable simulation of systems subject to noise, it is necessary to characterize the noise properly and develop efficient algorithms. In the first part of this talk, I will present an extension of KarhunenLoeve (KL) expansion to model and simulate multiple correlated random processes. The method finds the appropriate expansion for each correlated random process by releasing the biorthogonal condition of the KL expansion. I will address the convergence and computational efficiency, in addition to some explicit formulae and analytical results. In the remaining talk, I will discuss numerical methods to effectively compute the propagation of uncertainty in parameterized stochastic differential equations. Joint responseexcitation PDF equation generalizes the existing PDF equations and enables us to compute the PDF of the solution to system subject to nonGaussian colored noise. An adaptive discontinuous Galerkin method combined with probabilistic collocation method is developed to resolve both local and discontinuous dynamics, while lowrank tensor method is employed in case of highdimensionality. For anisotropic parameterized stochastic PDEs, we develop a reduced basis method using ANOVA decomposition to automatically identify the important dimensions and appropriate resolution in each dimension. The effectiveness of the methods is demonstrated in highdimensional stochastic PDEs.
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University of Maryland, College Park

Fri 25 Jan 2019, 3:00pm
Department Colloquium
ESB 2012

Mathematical modeling from singlecell data and its implications in cancer development and drug resistance

ESB 2012
Fri 25 Jan 2019, 3:00pm4:00pm
Abstract
Recent advances in singlecell gene sequencing data and highdimensional data analysis techniques are bringing in new opportunities in modeling biological systems. In this talk, I discuss different approaches to develop mathematical models from singlecell data. For highdimensional singlecell gene sequencing data, dimension reduction techniques are applied to find the trajectories of cell states in the reduced differentiation space, then modeled as directed and random movement on the abstracted graph with PDEs. Normal hematopoiesis differentiation and abnormal processes of acute myeloid leukemia (AML) progression are simulated, and the model can predict the emergence of cells in novel intermediate states of differentiation consistent with immunophenotypic characterizations of AML. In addition, we develop representations of multicorrelated stochastic processes for correlated time series cell data, by releasing the biorthogonal condition of KarhunenLoeve expansion. Convergence and computational efficiency of the methods are addressed. Finally, for fluorescence in situ hybridization data that provides spatialtemporal patterns of cells, we develop tumor growth model incorporating dynamics of drug resistance. It is demonstrated that assuming continuous cell state may result in different dynamics of anticancer drug resistance when compared with the predictions of classical discrete models, and its implications in designing therapies are studied.
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University of Alberta

Mon 28 Jan 2019, 4:00pm
Algebraic Geometry Seminar
MATH 126

Multiplicityfree products of Schubert divisors

MATH 126
Mon 28 Jan 2019, 4:00pm5:00pm
Abstract
Let G/B be a flag variety over C, where G is a simple algebraic group
with a simply laced Dynkin diagram, and B is a Borel subgroup. The
Bruhat decomposition of G defines subvarieties of G/B called Schubert
subvarieties. The codimension 1 Schubert subvarieties are called
Schubert divisors. The Chow ring of G/B is generated as an abelian
group by the classes of all Schubert varieties, and is "almost"
generated as a ring by the classes of Schubert divisors. More
precisely, an integer multiple of each element of G/B can be written
as a polynomial in Schubert divisors with integer coefficients. In
particular, each product of Schubert divisors is a linear combination
of Schubert varieties with integer coefficients.
In the first part of my talk I am going to speak about the
coefficients of these linear combinations. In particular, I am going
to explain how to check if a coefficient of such a linear combination
is nonzero and if such a coefficient equals 1. In the second part
of my talk, I will say something about an application of my result,
namely, how it makes it possible estimate socalled canonical
dimension of flag varieties and groups over nonalgebraicallyclosed
fields.
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Stanford University

Mon 28 Jan 2019, 4:00pm
Department Colloquium
MATH 100

Large deviations for sparse random graphs

MATH 100
Mon 28 Jan 2019, 4:00pm5:00pm
Abstract
Let G=G(N,p) be an Erd\H{o}sR\'enyi graph on N vertices (where each pair is connected by an edge independently with probability p). We view N as going to infinity, with p possibly going to zero with N. What is the probability that G contains twice as many triangles as we would expect? I will discuss recent progress on this ``infamous upper tail" problem, and more generally on tail estimates for counts of any fixed subgraph. These problems serve as a test bed for the emerging theory of \emph{nonlinear large deviations}, and also connect with issues in extending the theory of \emph{graph limits} to handle sparse graphs. In particular, I will discuss our approach to the upper tail problems via new versions of the classic regularity and counting lemmas from extremal combinatorics, specially tailored to the study of random graphs in the large deviations regime. This talk is based on joint work with Amir Dembo.
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Mathematics, UBC

Tue 29 Jan 2019, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS lounge)

Parameter Instability Regimes in Sparse Proximal Denoising Programs

ESB 4133 (PIMS lounge)
Tue 29 Jan 2019, 12:30pm1:30pm
Abstract
Compressed sensing theory explains why Lasso programs recover structured highdimensional signals with minimax orderoptimal error. Yet, the optimal choice of the program’s governing parameter is often unknown in practice. It is still unclear how variation of the governing parameter impacts recovery error in compressed sensing, which is otherwise provably stable and robust. We establish a novel notion of instability in Lasso programs when the measurement matrix is identity. This is the proximal denoising setup. We prove asymptotic cusplike behaviour of the risk as a function of the parameter choice, and illustrate the theory with numerical simulations. For example, a 0.1% underestimate of a Lasso parameter can increase the error significantly; and a 50% underestimate can cause the error to increase by a factor of 109. We hope that revealing parameter instability regimes of Lasso programs helps to inform a practitioner’s choice. Finally, we discuss how these results extend to their more general Lasso counterparts.
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Stanford University

Tue 29 Jan 2019, 3:30pm
Probability Seminar
MATH 126

Maximum of the characteristic polynomial for a random permutation matrix

MATH 126
Tue 29 Jan 2019, 3:30pm4:30pm
Abstract
Statistics of the characteristic polynomial for large Haar unitary matrices U at points on the unit circle have received considerable attention due to similarities with the statistics of the Riemann zeta function far up the critical axis. While the bestknown instances of this universality phenomenon concern statistics of \emph{zeros} for these functions (eigenvalues of U), there is strong evidence that the analogy also applies to extreme values.
Towards the more modest goal of understanding this universality phenomenon within the class of distributions on the unitary group, in this talk we consider the characteristic polynomial \chi_N(z) for an N\times N Haar permutation matrix. Our main result is a law of large numbers for (the logarithm of) the maximum modulus of \chi_N(z) over the unit circle. The main idea is to uncover a multiscale structure in the distribution of the random field \chi_N(z), and to adapt a wellknown second moment argument for the maximum of a branching random walk. Unlike the analogous problem for the Haar unitary, the distribution of \chi_N(z) is sensitive to Diophantine properties of the argument of z. To deal with this we borrow tools from the HardyLittlewood circle method in analytic number theory. Based on joint work with Ofer Zeitouni.
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Note for Attendees
Precolloquium refreshments will be served in MATH 125 at 3:45 p.m.