Princeton University

Mon 1 Oct 2018, 4:00pm
Institute of Applied Mathematics
ESB 2012

IAMPIMS Distinguished Colloquium: Symmetry, bifurcation, and multiagent decisionmaking

ESB 2012
Mon 1 Oct 2018, 4:00pm5:00pm
Abstract
I will present nonlinear dynamics for distributed decisionmaking that derive from principles of symmetry and bifurcation. Inspired by studies of animal groups, including househunting 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 multiagent 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, 4:00pm5:00pm
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, CohenMacaulay, 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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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, QuasiCycle Phase Synchronization

ESB 4133 (PIMS Lounge)
Tue 2 Oct 2018, 12:30pm1:30pm
Abstract
A latticeindexed family of stochastic processes has quasicycle oscillations if its otherwisedamped oscillations are sustained by noise. Such a family performs the reaction part of a stochastic reactiondiffusion system when we insert a local Mexican Hattype, difference of Gaussians, coupling on a onedimensional and on a twodimensional lattice. In one dimension we find that the phases of the quasicycles 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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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, 3:30pm4:30pm
Abstract
Selfsimilar 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 selfsimilar solutions and translating solitons for the mean curvature flow (MCF) and give rigidity results of some of them. We also investigate selfsimilar 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 BalogSzemerédiGowers theorem

ESB 4127
Tue 2 Oct 2018, 4:00pm5:00pm
Abstract
This is the first of a two part expository talk on the BalogSzemerédiGowers 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 fourmanifolds

ESB 4133 (PIMS lounge)
Wed 3 Oct 2018, 2:50pm3:45pm
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 fourmanifolds homotopy equivalent to surfaces.
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School of Interdisciplinary Mathematical Sciences (IMS), Meiji University

Wed 3 Oct 2018, 3:00pm
Mathematical Biology Seminar
ESB 4127

Derivation of replicatormutator equation as a limit of individualbased simulations

ESB 4127
Wed 3 Oct 2018, 3:00pm4:00pm
Abstract
We introduce a Markov chain model to study evolution of a continuous trait based on population genetics. It corresponds to individualbased model which includes frequency dependent selection caused by mplayer 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 replicatormutator equations. Our result establishes an affirmative mathematical base to the adaptive dynamics formulation employed in the theory of the mathematical biology.
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BenGurion University

Wed 3 Oct 2018, 4:00pm
Probability Seminar
ESB 2012

On polynomial vs. superpolynomial growth for finitely generated groups and harmonic functions

ESB 2012
Wed 3 Oct 2018, 4:00pm5:00pm
Abstract
I will discuss results and open problems about harmonic functions for finitely generated groups, with an emphasis on polynomial vs. superpolynomial 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, 4:00pm5:00pm
Abstract
The affine Grassmannian, though a somewhat esoteric looking object at first sight, is a fundamental algebrogeometric 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.
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MIT

Tue 9 Oct 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
MATH 105

Minimal surfaces and the AllenCahn equation on 3 manifolds

MATH 105
Tue 9 Oct 2018, 3:30pm4:30pm
Abstract
The AllenCahn equation is a semilinear 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 AllenCahn minmax construction in a 3manifold. Our results imply, for example, that in a 3manifold with a generic metric, for every positive integer p, there is an embedded twosided 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 BalogSzemerédiGowers theorem

ESB 4127
Tue 9 Oct 2018, 4:00pm5:00pm
Abstract
This is the second of a two part expository talk on the BalogSzemerédiGowers 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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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

ESB 4127
Wed 10 Oct 2018, 3:00pm4:00pm
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University of British Columbia

Wed 10 Oct 2018, 4:00pm
Probability Seminar
ESB 2012

Renormalization of local times of superBrownian motion

ESB 2012
Wed 10 Oct 2018, 4:00pm5:00pm
Abstract
For the local time L_t^x of superBrownian 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\pix)^{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, 4:00pm5:00pm
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 algebraictopological 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.
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Oregon

Mon 15 Oct 2018, 4:00pm
Algebraic Geometry Seminar
Math 126

Exoflops

Math 126
Mon 15 Oct 2018, 4:00pm5:00pm
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, 4:00pm5:00pm
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 mrowed 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, 2:50pm3:50pm
Abstract
The main goal of this talk is to introduce transitionally commutative principal Gbundles 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 Gbundles 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, 3:00pm3:45pm
Abstract
A traditional populationgenetics 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 forwardintime and the other is based on backwardintime 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.
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University of British Columbia

Wed 17 Oct 2018, 4:00pm
Probability Seminar
ESB 2012

The DobrushinLanfordRuelle theorem on steroids

ESB 2012
Wed 17 Oct 2018, 4:00pm5:00pm
Abstract
The DobrushinLanfordRuelle theorem gives sufficient
conditions on sets of configurations on the ddimensional 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 GómezAíza, Brian Marcus and Siamak Taati.
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Fri 19 Oct 2018, 12:00pm
Graduate Student Seminar
MATX 1115

Dyson Brownian motion: From random matrices to systems of noncolliding particles

MATX 1115
Fri 19 Oct 2018, 12:00pm1:00pm
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 onedimensional 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

CRMFieldsPIMS prize lecture: The KPZ fixed point

ESB 2012
Fri 19 Oct 2018, 4:00pm5:00pm
Abstract
The (1d) KPZ universality class contains random growth models, directed random polymers, stochastic HamiltonJacobi equations (e.g. the eponymous KardarParisiZhang 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).
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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, 4:05pm5:05pm
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 Ktheory 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, 12:00pm1:00pm
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 NPhard 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.
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UBC

Tue 23 Oct 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
MATH 105

Global NavierStokes flows for nondecaying initial data with slowly decaying oscillation

MATH 105
Tue 23 Oct 2018, 3:30pm4:30pm
Abstract
We consider the Cauchy problem of 3D incompressible NavierStokes equations for uniformly locally square integrable initial data. The existence of a timeglobal weak solution has been known, when the square integral of the initial datum on a ball vanishes as the ball goes to infinity. For nondecaying 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 nondecaying initial data whose local oscillations slowly decay.
This is a joint work with TaiPeng Tsai.
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UBC

Tue 23 Oct 2018, 4:00pm
Discrete Math Seminar
ESB 4127

The TriangleFree Process

ESB 4127
Tue 23 Oct 2018, 4:00pm5:00pm
Abstract
This is the first part of a two part exposition on the triangleprocess. The trianglefree 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 trianglefree 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 trianglefree process and the oddcyclefree 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, 3:00pm3:45pm
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 postvaccination balance of serotypes would present the opportunity to achieve a final population composed of the most benign (noninvasive) strains. However, the complex ecology of the pneumococcus makes it difficult to predict the postvaccination balance of strains. Recently, Corander et al proposed that there is widespread apparent negative frequencydependent 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 outperform 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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Wed 24 Oct 2018, 4:00pm
Probability Seminar
ESB 2012

TBA

ESB 2012
Wed 24 Oct 2018, 4:00pm5:00pm
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, 4:00pm5:00pm
Abstract
In this talk I will discuss joint work with J. Achter and C. Vial showing that the image of the AbelJacobi 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, 3:00pm3:45pm
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 spatiotemporal description of chikungunya spread using a cellular automata over unstructured triangular meshes.
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Note for Attendees
Refreshments (PIMS Tea) are served at 2:45PM in the PIMS lounge.