Mathematics Dept.
  Events
Princeton University
Mon 1 Oct 2018, 4:00pm
Institute of Applied Mathematics
ESB 2012
IAM-PIMS Distinguished Colloquium: Symmetry, bifurcation, and multi-agent decision-making
ESB 2012
Mon 1 Oct 2018, 4:00pm-5:00pm

Abstract

I will present nonlinear dynamics for distributed decision-making that derive from principles of symmetry and bifurcation. Inspired by studies of animal groups, including house-hunting honeybees and schooling fish, the nonlinear dynamics describe a group of interacting agents that can manage flexibility as well as stability in response to a changing environment.

Naomi Ehrich Leonard is Edwin S. Wilsey Professor of Mechanical and Aerospace Engineering and associated faculty in Applied and Computational Mathematics at Princeton University. She is a MacArthur Fellow, and Fellow of the American Academy of Arts and Sciences, SIAM, IEEE, IFAC, and ASME. She received her BSE in Mechanical Engineering from Princeton University and her PhD in Electrical Engineering from the University of Maryland. Her research is in control and dynamics with application to multi-agent systems, mobile sensor networks, collective animal behavior, and human decision dynamics.

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Northeastern
Mon 1 Oct 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126
The Conormal Variety of a Schubert Variety
MATH 126
Mon 1 Oct 2018, 4:00pm-5:00pm

Abstract

Let N be the conormal variety of a Schubert variety X. In this talk, we discuss the geometry of N in two cases, when X is cominuscule, and when X is a divisor. In particular, we present a resolution of singularities and a system of defining equations for N, and also describe certain cases when N is normal, Cohen-Macaulay, and Frobenius split. Time permitting, we will also illustrate the close relationship between N and orbital varieties, and discuss the consequences of the above constructions for orbital varieties.
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Lawrence Ward
Department of Psychology and Brain Research Centre, UBC
Tue 2 Oct 2018, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Rapidly Forming, Slowly Evolving, Quasi-Cycle Phase Synchronization
ESB 4133 (PIMS Lounge)
Tue 2 Oct 2018, 12:30pm-1:30pm

Abstract

A lattice-indexed family of stochastic processes has quasi-cycle oscillations if its otherwise-damped oscillations are sustained by noise. Such a family performs the reaction part of a stochastic reaction-diffusion system when we insert a local Mexican Hat-type, difference of Gaussians, coupling on a one-dimensional and on a two-dimensional lattice. In one dimension we find that the phases of the quasi-cycles synchronize (establish a relatively constant relationship, or phase locking) rapidly at coupling strengths lower than those required to produce spatial patterns of their amplitudes. The patterns of phase locking persist and evolve but do not induce patterns in the amplitudes. In two dimensions the amplitude patterns form more quickly, but there remain parameter regimes in which phase patterns form without being accompanied by clear amplitude patterns. At higher coupling strengths we find patterns both of phase synchronization and of amplitude (resembling Turing patterns) corresponding to the patterns of phase synchronization. Specific properties of these patterns are controlled by the parameters of the reaction and of the Mexican Hat coupling.
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Juncheol Pyo
Pusan National University and UBC
Tue 2 Oct 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
MATH 105
Solitons for the mean curvature flow and inverse mean curvature flow
MATH 105
Tue 2 Oct 2018, 3:30pm-4:30pm

Abstract

 Self-similar solutions and translating solitons are not only special solutions of mean curvature flow (MCF) but a key role in the study of singularities of MCF. They have received a lot of attention. We introduce some examples of self-similar solutions and translating solitons for the mean curvature flow (MCF) and give rigidity results of some of them. We also investigate self-similar solutions and translating solitons to the inverse mean curvature flow (IMCF) in Euclidean space. 
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UBC
Tue 2 Oct 2018, 4:00pm
Discrete Math Seminar
ESB 4127
An exposition of the Balog-Szemerédi-Gowers theorem
ESB 4127
Tue 2 Oct 2018, 4:00pm-5:00pm

Abstract

This is the first of a two part expository talk on the Balog-Szemerédi-Gowers theorem. This theorem, originally due to Balog and Szemerédi and later strengthened by Gowers, is one of the most important tools in additive combinatorics, with applications ranging from additive number theory to combinatorial geometry and harmonic analysis. In part one we will motivate the result by highlighting its importance and usefulness. In part two we will present a proof of the result. The proof that we present is a variant of Gowers’ graph theoretic proof, due to Sudakov, Szemerédi and Vu.
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North Carolina State University
Wed 3 Oct 2018, 2:50pm
Topology and related seminars
ESB 4133 (PIMS lounge)
Spines in four-manifolds
ESB 4133 (PIMS lounge)
Wed 3 Oct 2018, 2:50pm-3:45pm

Abstract

Given two homotopy equivalent manifolds with different dimensions, it is natural to ask if the smaller one embeds in the larger one. We will discuss this problem in the case of four-manifolds homotopy equivalent to surfaces. 
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Joe Yuichiro Wakano
School of Interdisciplinary Mathematical Sciences (IMS), Meiji University
Wed 3 Oct 2018, 3:00pm
Mathematical Biology Seminar
ESB 4127
Derivation of replicator-mutator equation as a limit of individual-based simulations
ESB 4127
Wed 3 Oct 2018, 3:00pm-4:00pm

Abstract

We introduce a Markov chain model to study evolution of a continuous trait based on population genetics. It corresponds to individual-based model which includes frequency dependent selection caused by m-player game interactions and stochastic fluctuations due to random genetic drift and mutation. We prove that under a proper scaling limit as the population size increases the system converges to the solution of replicator-mutator equations. Our result establishes an affirmative mathematical base to the adaptive dynamics formulation employed in the theory of the mathematical biology.

Note for Attendees

 Refreshments (PIMS Tea) are served at 2:45PM in the PIMS lounge.
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Tom Meyerovitch
Ben-Gurion University
Wed 3 Oct 2018, 4:00pm
Probability Seminar
ESB 2012
On polynomial vs. super-polynomial growth for finitely generated groups and harmonic functions
ESB 2012
Wed 3 Oct 2018, 4:00pm-5:00pm

Abstract

 I will discuss results and open problems about harmonic functions for finitely generated groups, with an emphasis on polynomial vs. super-polynomial growth. By "polynomial growth" I am implying to at least two different notions:
1. The volume growth of balls in the group (with respect to the word metric).
2. The growth of the sup norm of a harmonic function on a ball.
The investigation is partly motivated by Kleiner’s proof for Gromov’s theorem on groups of polynomial growth, by Ozawa's more recent proof of Gromov's theorem and by some related conjectures and hypothetical future applications to problems in geometric group theory.
Most of the results I will present in this talk will be at least a few years old and based on joint work with Ariel Yadin and Perl, Tointon and Yadin.
      
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UBC Math
Fri 5 Oct 2018, 4:00pm
Department Colloquium
ESB 2012
Cluster theory of the coherent Satake category
ESB 2012
Fri 5 Oct 2018, 4:00pm-5:00pm

Abstract

The affine Grassmannian, though a somewhat esoteric looking object at first sight, is a fundamental algebro-geometric construction lying at the heart of a series of ideas connecting number theory (and the Langlands program) to geometric representation theory, low dimensional topology and mathematical physics.

Historically it is popular to study the category of constructible perverse sheaves on the affine Grassmannian. This leads to the *constructible* Satake category and the celebrated (geometric) Satake equivalence.

More recently it has become apparent that it makes sense to also study the category of perverse *coherent* sheaves (the coherent Satake category). Motivated by certain ideas in mathematical physics this category is conjecturally governed by a cluster algebra structure.

We will illustrate the geometry of the affine Grassmannian in an elementary way, discuss what we mean by a cluster algebra structure and then describe a solution to this conjecture in the case of general linear groups.

Note for Attendees

Refreshments will be served in ESB 4133 from 3:45 p.m.-4:00 p.m.
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MIT
Tue 9 Oct 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
MATH 105
Minimal surfaces and the Allen-Cahn equation on 3 manifolds
MATH 105
Tue 9 Oct 2018, 3:30pm-4:30pm

Abstract

   The Allen--Cahn equation is a semi-linear PDE that produces minimal surfaces via a certain singular limit. We will describe recent work proving index, multiplicity, and curvature estimates in the context of an Allen--Cahn min-max construction in a 3-manifold. Our results imply, for example, that in a 3-manifold with a generic metric, for every positive integer p, there is an embedded two-sided minimal surface of Morse index p. This is joint with Otis Chodosh.
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UBC
Tue 9 Oct 2018, 4:00pm
Discrete Math Seminar
ESB 4127
An exposition of the Balog-Szemerédi-Gowers theorem
ESB 4127
Tue 9 Oct 2018, 4:00pm-5:00pm

Abstract

This is the second of a two part expository talk on the Balog-Szemerédi-Gowers theorem. This theorem, originally due to Balog and Szemerédi and later strengthened by Gowers, is one of the most important tools in additive combinatorics, with applications ranging from additive number theory to combinatorial geometry and harmonic analysis. In part one we will motivate the result by highlighting its importance and usefulness. In part two we will present a proof of the result. The proof that we present is a variant of Gowers’ graph theoretic proof, due to Sudakov, Szemerédi and Vu.

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James J. Feng
Department of Mathematics, Department of Chemical and Biological Engineering, University of British
Wed 10 Oct 2018, 3:00pm
ESB 4127
Spontaneous collective migration of neural crest cells
University of British Columbia
Wed 10 Oct 2018, 4:00pm
Probability Seminar
ESB 2012
Renormalization of local times of super-Brownian motion
ESB 2012
Wed 10 Oct 2018, 4:00pm-5:00pm

Abstract

For the local time L_t^x of super-Brownian motion X starting from \delta_0, we study its asymptotic behavior as x\to 0. In d=3, we find a normalization \psi(x)=((2\pi^2)^{-1} \log (1/|x|))^{1/2} such that (L_t^x-(2\pi|x|)^{-1})/\psi(x) converges in distribution to standard normal as x\to 0. In d=2, we show that L_t^x-\pi^{-1} \log (1/|x|) converges a.s. as x\to 0. We also consider general initial conditions and get some renormalization results. The behavior of the local time allows us to derive a second order term in the asymptotic behavior of a related semilinear elliptic equation.   
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UBC Math
Fri 12 Oct 2018, 4:00pm
Department Colloquium
ESB 2012
PIMS/ UBC Math Faculty Award Colloquium: The topology of Azumaya algebras
ESB 2012
Fri 12 Oct 2018, 4:00pm-5:00pm

Abstract

Azumaya algebras over a commutative ring R are generalizations of central simple algebras over a field k, and both are "twisted matrix algebras". In this, they bear the same relationship to a noncommutative ring of matrices Mat_n(k) that a vector bundles (or projective modules) bear to vector spaces. That is, they are bundles of algebras. In this talk, I will show that thinking about Azumaya algebras from the algebraic-topological point of view, as bundles of algebras, is fruitful, both in producing examples of algebras with interesting properties, and in proving certain results about such algebras that are difficult to prove by direct, algebraic methods.
 

Note for Attendees

Refreshments will be served in ESB 4133 from 3:45 p.m.-4:00 p.m.
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Oregon
Mon 15 Oct 2018, 4:00pm
Algebraic Geometry Seminar
Math 126
Exoflops
Math 126
Mon 15 Oct 2018, 4:00pm-5:00pm

Abstract

The derived category of a hypersurface is equivalent to the 
category of matrix factorizations of a certain function on the total space 
of a line bundle over the ambient space.  The hypersurface is smooth if 
and only if the critical locus of the function is compact.  I will present 
a construction through which a resolution of singularities of the 
hypersurface corresponds to a compactification of the critical locus of 
the function, which can be very interesting in examples.  This is joint 
work with Paul Aspinwall and Ed Segal.
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UBC
Tue 16 Oct 2018, 4:00pm
Discrete Math Seminar
ESB 4127
(0,1,2)-matrices can sometimes behave like (0,1)-matrices
ESB 4127
Tue 16 Oct 2018, 4:00pm-5:00pm

Abstract

 This is joint work with Jeffrey Dawson, Linyuan Lu and Attila Sali.
 
We define simple matrices as those whose entries are chosen from {0,1,2} and for which no columns are repeated.  We consider the extremal problem of how many columns can an m-rowed simple matrix A have, subject to the condition that A avoids certain submatrices.  
 
We consider some forbidden submatrices (configurations) that seem to force A to behave like a (0,1)-matrix.  Define T_k(a,b,c) to be the kxk matrix with b's on the diagonal, a's below the diagonal and c's above the diagonal. These generalize the identity and triangular matrices. There are such 8 matrices to forbid which seem to force A to behave like a (0,1)-matrix. Some preliminary results are given.
 
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Universidad Nacional de Colombia sede Medellín
Wed 17 Oct 2018, 2:50pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Transitionally commutative bundles
ESB 4133 (PIMS Lounge)
Wed 17 Oct 2018, 2:50pm-3:50pm

Abstract

The main goal of this talk is to introduce transitionally commutative principal G-bundles and to show that they can be classified homotopically using a space B_comG that is called the classifying space for commutativity in G. In the second half of the talk I provide some examples of bundles that are trivial as principal G-bundles but not as transitionally commutative bundles.
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Dept of Evolutionay Studies of Biosystems, The Graduate University for Advanced Studies (SOKENDAI), Japan
Wed 17 Oct 2018, 3:00pm
Mathematical Biology Seminar
ESB 4127
Allele frequency spectrum in a cancer cell population
ESB 4127
Wed 17 Oct 2018, 3:00pm-3:45pm

Abstract

A traditional population-genetics approach studies geneaologies in a population of a fixed size, which forms the basis of several spectral theories of finite samples. In contrast, a population of tumor cells typically experiences an exponential growth phase in its initial progression, which is far from constant population size. In this work, I develop two different numerical procedures, one of which is based on forward-in-time and the other is based on backward-in-time treatment, to derive allele frequency spectrum in such exponentially growing cancer cell populations. We find significance bias toward singletons both analytically and numerically, which reflects the fact that most observed mutations have recent origins in a growing population.

This work was done in collaboration with Prof. Hideki Innan.

Note for Attendees

The seminar is followed by PIMS tea at 3:45pm.
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University of British Columbia
Wed 17 Oct 2018, 4:00pm
Probability Seminar
ESB 2012
The Dobrushin-Lanford-Ruelle theorem on steroids
ESB 2012
Wed 17 Oct 2018, 4:00pm-5:00pm

Abstract

The Dobrushin-Lanford-Ruelle theorem gives sufficient 
conditions on sets of configurations on the d-dimensional lattice so 
that (1) every measure which maximizes the topological pressure is a 
Gibbs measure and (2) every Gibbs measure maximizes the topological 
pressure. In this talk we shall discuss a generalization of this theorem 
in several directions: the lattice is now an arbitrary countable 
amenable group, we permit the existence of a random environment and 
consider measures that project onto it, and we relax the required 
conditions of (1) to a much larger class of dynamical systems. We shall 
also present a few applications of this theorem.
 
This is joint work with Ricardo Gómez-Aíza, Brian Marcus and Siamak Taati.
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Thomas Hughes
Fri 19 Oct 2018, 12:00pm
Graduate Student Seminar
MATX 1115
Dyson Brownian motion: From random matrices to systems of non-colliding particles
MATX 1115
Fri 19 Oct 2018, 12:00pm-1:00pm

Abstract

In this talk I will introduce Dyson Brownian motion. Roughly put, this is a stochastic process given by the eigenvalues of an (N x N) Hermitian matrix whose entries are Brownian motions. I will discuss its connection to random matrix theory and give several other descriptions of the process: these include, on one hand, a system of stochastic differential equations with repulsive drift, and on the other, the distribution of N one-dimensional Brownian motions that are conditioned not to collide.
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University of Toronto
Fri 19 Oct 2018, 4:00pm
Department Colloquium
ESB 2012
CRM-Fields-PIMS prize lecture: The KPZ fixed point
ESB 2012
Fri 19 Oct 2018, 4:00pm-5:00pm

Abstract

The (1d) KPZ universality class contains random growth models, directed random polymers, stochastic Hamilton-Jacobi equations (e.g. the eponymous Kardar-Parisi-Zhang equation). It is characterized by unusual scale of fluctuations, some of which appeared earlier in random matrix theory, and which depend on the initial data. The explanation is that on large scales everything approaches a special scaling invariant Markov process, the KPZ fixed point. It is obtained by solving one model in the class, TASEP, and passing to the limit. Both TASEP and the KPZ fixed point turn out to have a novel structure: "stochastic integrable systems" (Joint work with Konstantin Matetski and Daniel Remenik).

Note for Attendees

Refreshments will be served in ESB 4133 from 3:45 p.m.-4:00 p.m.
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UBC
Mon 22 Oct 2018, 4:05pm
Algebraic Geometry Seminar
MATH 126
Bivariant Theories and Algebraic Cobordism of Singular Varieties
MATH 126
Mon 22 Oct 2018, 4:05pm-5:05pm

Abstract

I will outline the construction of a natural bivariant theory extending algebraic bordism, which will yield an extension of algebraic cobordism to singular varieties. I will also discuss the connections of this theory to algebraic K-theory and to intersection theory.
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Department of Mathematics, University of Waterloo
Tue 23 Oct 2018, 12:00pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge) Please note it starts 30 mins. earlier than the usual time.
Solving DNN Relaxations of the Quadratic Assignment Problem with ADMM and Facial Reduction
ESB 4133 (PIMS Lounge) Please note it starts 30 mins. earlier than the usual time.
Tue 23 Oct 2018, 12:00pm-1:00pm

Abstract

The quadratic assignment problem, QAP, has many applications ranging from the planning of building locations of a university, to the positioning of modules on a computer chip (VLSI design), to the design of keyboards. This problem is arguably one of the hardest of the NP-hard problems, as problems with dimension 30 are still considered hard to solve to optimality.

The QAP in the trace formulation is modelled as the minimization of a quadratic function over the permutation matrices. The set of permutation matrices can be represented by quadratic constraints. Relaxations of these constraints are used in branch and bound solution methods. These relaxations include the eigenvalue and projected eigenvalue relaxations, as well as various semidefinite programming, SDP,  and doubly nonnegative, DNN, relaxations. These latter relaxations are particularly strong and often solve the QAP to optimality. However, they can be extremely expensive to solve.

 We show that the combination of an alternating directions method of multipliers, ADMM, in combination with facial reduction works extremely well in solving the very difficult DNN relaxation.

Note for Attendees

Sushi will be served.
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Hyunju Kwon
UBC
Tue 23 Oct 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
MATH 105
Global Navier-Stokes flows for non-decaying initial data with slowly decaying oscillation
MATH 105
Tue 23 Oct 2018, 3:30pm-4:30pm

Abstract

We consider the Cauchy problem of 3D incompressible Navier-Stokes equations for uniformly locally square integrable initial data. The existence of a time-global weak solution has been known, when the square integral of the initial datum on a ball vanishes as the ball goes to infinity. For non-decaying data, however, the only known global solutions are either for perturbations of constants or when the velocity gradients are in Lp with finite p. In this talk, I will outline how to construct global weak solutions for general non-decaying initial data whose local oscillations slowly decay.
This is a joint work with Tai-Peng Tsai.
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Ethan White
UBC
Tue 23 Oct 2018, 4:00pm
Discrete Math Seminar
ESB 4127
The Triangle-Free Process
ESB 4127
Tue 23 Oct 2018, 4:00pm-5:00pm

Abstract

This is the first part of a two part exposition on the triangle-process. The triangle-free process begins on an empty graph and adds edges at random, provided no triangle is created with the existing edges. One of the original motivations for the process came from Ramsey Theory. Spencer conjectured that the maximum size of an independent set in a graph resulting from the process should be relatively small, and so the triangle-free process would provide constructions for lower bounds on the Ramsey number R(3,t). Recently, Bohman and Keevash obtained new estimates on independence number of such graphs, which gives a lower bound on R(3,t) within a factor of 4+o(1) of the best know upper bound. 

In this first part we will introduce random graph processes with an emphasis on the triangle-free process and the odd-cycle-free process.



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Mathematics, SFU
Wed 24 Oct 2018, 3:00pm
Mathematical Biology Seminar
ESB 4127
Connecting genomic data with vaccine design through modelling
ESB 4127
Wed 24 Oct 2018, 3:00pm-3:45pm

Abstract


While vaccines are available and are effective in protecting against colonisation and disease with Streptococcus pneumoniae, their effectiveness is limited by strain (serotype) replacement following widespread vaccination. Understanding the post-vaccination balance of serotypes would present the opportunity to achieve a final population composed of the most benign (non-invasive) strains. However, the complex ecology of the pneumococcus makes it difficult to predict the post-vaccination balance of strains. Recently, Corander et al proposed that there is widespread apparent negative frequency-dependent selection (NFDS) in the pneumococcus (Corander et al 2017 Nat. Ecol. Evol.).

Here, we use this principle to develop a deterministic model of pneumococcal strain dynamics, and use the model to make predictions about the ecological response of the pneumococcal population to new candidate vaccine strategies. We find that we can identify formulations that out-perform existing formulations in the model. Furthermore, it is possible to obtain a final model population that scores as well as the currently used formulation, using a vaccine strategy with fewer serotypes -- these formulations would be much less costly to produce than current vaccines. We suggest that this approach could provide a template for principled vaccine design based on global surveillance data and genomics.

This is joint work with N. Croucher.
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Ander Holroyd
Wed 24 Oct 2018, 4:00pm
Probability Seminar
ESB 2012
TBA
ESB 2012
Wed 24 Oct 2018, 4:00pm-5:00pm

Abstract


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University of Colorado
Mon 29 Oct 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126
Distinguished models of intermediate Jacobians
MATH 126
Mon 29 Oct 2018, 4:00pm-5:00pm

Abstract

In this talk I will discuss joint work with J. Achter and C. Vial showing that the image of the Abel--Jacobi map on algebraically trivial cycles descends to the field of definition for smooth projective varieties defined over subfields of the complex numbers. The main focus will be on applications to topics such as: descending cohomology geometrically, a conjecture of Orlov regarding the derived category and Hodge theory, and motivated admissible normal functions.
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Professor Gerardo Ortigoza
Universidad Veracruzana Mexico
Wed 31 Oct 2018, 3:00pm
Mathematical Biology Seminar
ESB 4127
Mathematical modeling and simulation of the Chikungunya spread in Veracruz Mexico
ESB 4127
Wed 31 Oct 2018, 3:00pm-3:45pm

Abstract

 Chikungunya is a viral disease transmitted to humans by infected mosquitoes: Aedes aegypti and Aedes albopictus. It causes fever and severe joint pain. Other symptoms include muscle pain, headache, nausea, fatigue and rash. Joint pain is often debilitating and can vary in duration. 
Some of the main mathematical methods to simulate Chikungunya
spread are set as ordinary differential equations over compartmental models, SEIR for host and sei for vectors. We propose a spatio-temporal description of chikungunya spread using a cellular automata over unstructured triangular meshes.

Note for Attendees

 The seminar is followed by PIMS Tea at 3:45pm
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