Complete Schedule of Talks
Thursday, July 26, 2018 
8:00am  9:00am 
Breakfast and Registration (Cox Science Veranda) 
9:00am  9:30am 
Welcome (Cox Science Bldg., Room 145) 
9:30am  10:45am 
Victor Reiner, Finite Reflection Groups and General Linear Groups, Part I
(Cox Science Bldg., Room 145) 
10:45am  11:15am 
Coffee Break (Cox Science Veranda) 
11:15am  12:30pm 
Victor Reiner, Finite Reflection Groups and General Linear Groups, Part II
(Cox Science Bldg., Room 145) 
12:30pm  2:00pm 
Lunch (Cox Science Veranda) 
2:00pm  2:45pm 
Special Session Talks, Part I
Algebraic Geometry: Ernesto Lupercio (Memorial Bldg., Room 211)
Combinatorics: Stephanie van Willigenburg (Memorial Bldg., Room 312)
Differential Geometry: Lu Wang (Memorial Bldg., Room 313)
Mathematical Biology: Xi Huo (Memorial Bldg., Room 315) 
2:45pm  3:00pm 
Coffee Break (Cox Science Veranda) 
3:00pm  3:45pm 
Special Session Talks, Part II
Algebraic Geometry: Andrew Harder (Memorial Bldg., Room 211)
Combinatorics: Carolina Benedetti (Memorial Bldg., Room 312)
Differential Geometry: Martín Reiris (Memorial Bldg., Room 313)
Mathematical Biology: Jorge VelascoHernandez (Memorial Bldg., Room 315) 
3:45pm  4:00pm 
Coffee Break (Cox Science Veranda) 
4:00pm  4:45pm 
Special Session Talks, Part III
Algebraic Geometry: Bernardo Uribe (Memorial Bldg., Room 211)
Combinatorics: Alejandro Morales (Memorial Bldg., Room 312)
Differential Geometry: Chao Li (Memorial Bldg., Room 313)
Mathematical Biology: Zhisheng Shuai (Memorial Bldg., Room 315) 
Friday, July 27, 2018 
8:30am  9:30am 
Breakfast and Registration (Cox Science Lobby) 
9:30am  10:45am 
Mark Lewis, Population Dynamics in Moving Environments, Part I
(Cox Science Bldg., Room 145) 
10:45am  11:15am 
Coffee Break (Cox Science Lobby) 
11:15am  12:30pm 
Mark Lewis, Population Dynamics in Moving Environments, Part II
(Cox Science Bldg., Room 145) 
12:30pm  2:00pm 
Lunch (Cox Science Lobby) 
2:00pm  2:45pm 
Special Session Talks, Part IV
Algebraic Geometry: Gabriel Kerr (Memorial Bldg., Room 211)
Combinatorics: John Shareshian (Memorial Bldg., Room 312)
Differential Geometry: Robert Haslhofer (Memorial Bldg., Room 313)
Mathematical Biology: KingYeung Lam (Memorial Bldg., Room 315) 
2:45pm  3:00pm 
Coffee Break (Cox Science Lobby) 
3:00pm  3:45pm 
Special Session Talks, Part V
Algebraic Geometry: Richard (Paul) Horja (Memorial Bldg., Room 211)
Combinatorics: Rafael González D'León (Memorial Bldg., Room 312)
Differential Geometry: Christos Mantoulidis (Memorial Bldg., Room 313)
Mathematical Biology: Salomé Martínez (Memorial Bldg., Room 315) 
3:45pm  4:00pm 
Coffee Break (Cox Science Lobby) 
4:00pm  4:45pm 
Special Session Talks, Part VI
Algebraic Geometry: Andrei Teleman (Memorial Bldg., Room 211)
Combinatorics: Marcelo Aguiar (Memorial Bldg., Room 312)
Differential Geometry: Otis Chodosh (Memorial Bldg., Room 313)
Mathematical Biology: Nancy Rodriguez (Memorial Bldg., Room 315) 
7:30pm 
BANQUET – Shalala Student Center – Ballroom 3rd Floor 
Saturday, July 28, 2018 
8:00am  9:00am 
Breakfast (Cox Science Lobby) 
9:00am  10:15am 
Michael Eichmair, On Scalar Curvature, Minimal Surfaces, and the Isoperimetric Problem in the Large, Part I (Cox Science Bldg., Room 145) 
10:15am  10:45am 
Coffee Break 
10:45am  12:00pm 
Michael Eichmair, On Scalar Curvature, Minimal Surfaces, and the Isoperimetric Problem in the Large, Part II (Cox Science Bldg., Room 145) 
12:00pm  1:30pm 
Lunch (Cox Science Lobby) 
1:30pm  2:30pm 
Panel Discussion on Graduate Education (Cox Science Bldg., Room 145) 
2:30pm  2:45pm 
Coffee Break (Cox Science Lobby) 
2:45pm  3:30pm 
Special Session Talks, Part VII
Algebraic Geometry: Manuel Rivera (Memorial Bldg., Room 211)
Combinatorics: Sara Billey (Memorial Bldg., Room 312)
Differential Geometry: Lucas Ambrozio (Memorial Bldg., Room 313)
Mathematical Biology: Suzanne Lenhart (Memorial Bldg., Room 315) 
3:30pm  3:45pm 
Coffee Break (Cox Science Lobby) 
3:45pm  4:30pm 
Special Session Talks, Part VIII
Algebraic Geometry: Jacob Mostovoy (Memorial Bldg., Room 211)
Combinatorics: José Alejandro Samper Casas (Memorial Bldg., Room 312)
Differential Geometry: Siyuan Lu (Memorial Bldg., Room 313)
Mathematical Biology: Carlos CastilloChavez (Memorial Bldg., Room 315) 
4:30pm  4:45pm 
Coffee Break (Cox Science Lobby) 
4:45pm  5:30pm 
Special Session Talks, Part IX
Algebraic Geometry: Lino Grama (Memorial Bldg., Room 211)
Combinatorics: Patricia Hersh (Memorial Bldg., Room 312)
Differential Geometry: Abraão Mendes (Memorial Bldg., Room 313)
Mathematical Biology: Juan Gutierrez (Memorial Bldg., Room 315) 
Sunday, July 29, 2018 
8:00am  9:00am 
Breakfast (Cox Science Lobby) 
9:00am  10:15am 
Denis Auroux, An Invitation to Homological Symmetry, Part I
(Cox Science Bldg., Room 145) 
10:15am  10:45am 
Coffee Break (Cox Science Lobby) 
10:45am  12:00pm 
Denis Auroux, An Invitation to Homological Symmetry, Part II
(Cox Science Bldg., Room 145) 
12:00pm  1:00pm 
Lunch (Cox Science Lobby) 
1:00pm  2:00pm 
Yuri Tschinkel, Building Institutes, (Cox Science Bldg., Room 145) 
2:00pm 
Conference Farewell 
Plenary and Special Public Lectures
Thursday, July 26, 2018 
9:30am  10:45am 
Victor Reiner, Finite Reflection Groups and General Linear Groups, Part I
(Cox Science Bldg., Room 145) 
11:15am  12:30pm 
Victor Reiner, Finite Reflection Groups and General Linear Groups, Part II
(Cox Science Bldg., Room 145) 
Friday, July 27, 2018 
9:30am  10:45am 
Mark Lewis, Population Dynamics in Moving Environments, Part I
(Cox Science Bldg., Room 145) 
11:15am  12:30pm 
Mark Lewis, Population Dynamics in Moving Environments, Part II
(Cox Science Bldg., Room 145) 
Saturday, July 28, 2018 
9:00am  10:15am 
Michael Eichmair, On Scalar Curvature, Minimal Surfaces, and the Isoperimetric Problem in the Large, Part I (Cox Science Bldg., Room 145) 
10:45am  12:00pm 
Michael Eichmair, On Scalar Curvature, Minimal Surfaces, and the Isoperimetric Problem in the Large, Part II (Cox Science Bldg., Room 145) 
Sunday, July 29, 2018 
9:00am  10:15am 
Denis Auroux, An Invitation to Homological Symmetry, Part I
(Cox Science Bldg., Room 145) 
10:45am  12:00pm 
Denis Auroux, An Invitation to Homological Symmetry, Part II
(Cox Science Bldg., Room 145) 
1:00pm  2:00pm 
Yuri Tschinkel, Building Institutes, (Cox Science Bldg., Room 145) 
Algebraic Geometry and Topology
Thursday, July 26, 2018 
2:00pm  2:45pm 
Ernesto Lupercio (Memorial Bldg., Room 211) 
3:00pm  3:45pm 
Andrew Harder (Memorial Bldg., Room 211) 
4:00pm  4:45pm 
Bernardo Uribe (Memorial Bldg., Room 211) 
Friday, July 27, 2018 
2:00pm  2:45pm 
Gabriel Kerr (Memorial Bldg., Room 211) 
3:00pm  3:45pm 
Richard (Paul) Horja (Memorial Bldg., Room 211) 
4:00pm  4:45pm 
Andrei Teleman (Memorial Bldg., Room 211) 
Saturday, July 28, 2018 
2:45pm  3:30pm 
Manuel Rivera (Memorial Bldg., Room 211) 
3:45pm  4:30pm 
Jacob Mostovoy (Memorial Bldg., Room 211) 
4:45pm  5:30pm 
Lino Grama (Memorial Bldg., Room 211) 
Combinatorics
Thursday, July 26, 2018 
2:00pm  2:45pm 
Stephanie van Willigenburg (Memorial Bldg., Room 312) 
3:00pm  3:45pm 
Carolina Benedetti (Memorial Bldg., Room 312) 
4:00pm  4:45pm 
Alejandro Morales (Memorial Bldg., Room 312) 
Friday, July 27, 2018 
2:00pm  2:45pm 
John Shareshian (Memorial Bldg., Room 312) 
3:00pm  3:45pm 
Rafael González D'León (Memorial Bldg., Room 312) 
4:00pm  4:45pm 
Marcelo Aguiar (Memorial Bldg., Room 312) 
Saturday, July 28, 2018 
2:45pm  3:30pm 
Sara Billey (Memorial Bldg., Room 312) 
3:45pm  4:30pm 
José Alejandro Samper Casas (Memorial Bldg., Room 312) 
4:45pm  5:30pm 
Patricia Hersh (Memorial Bldg., Room 312) 
Differential Geometry and Geometric Analysis
Thursday, July 26, 2018 
2:00pm  2:45pm 
Lu Wang (Memorial Bldg., Room 313) 
3:00pm  3:45pm 
Martín Reiris (Memorial Bldg., Room 313) 
4:00pm  4:45pm 
Chao Li (Memorial Bldg., Room 313) 
Friday, July 27, 2018 
2:00pm  2:45pm 
Robert Haslhofer (Memorial Bldg., Room 313)

3:00pm  3:45pm 
Christos Mantoulidis (Memorial Bldg., Room 313) 
4:00pm  4:45pm 
Otis Chodosh (Memorial Bldg., Room 313) 
Saturday, July 28, 2018 
2:45pm  3:30pm 
Lucas Ambrozio (Memorial Bldg., Room 313) 
3:45pm  4:30pm 
Siyuan Lu (Memorial Bldg., Room 313) 
4:45pm  5:30pm 
Abraão Mendes (Memorial Bldg., Room 313) 
Mathematical Biology
Thursday, July 26, 2018 
2:00pm  2:45pm 
Xi Huo (Memorial Bldg., Room 315) 
3:00pm  3:45pm 
Jorge VelascoHernandez (Memorial Bldg., Room 315) 
4:00pm  4:45pm 
Zhisheng Shuai (Memorial Bldg., Room 315) 
Friday, July 27, 2018 
2:00pm  2:45pm 
KingYeung Lam (Memorial Bldg., Room 315) 
3:00pm  3:45pm 
Salomé Martínez (Memorial Bldg., Room 315) 
4:00pm  4:45pm 
Nancy Rodriguez (Memorial Bldg., Room 315) 
Saturday, July 28, 2018 
2:45pm  3:30pm 
Suzanne Lenhart (Memorial Bldg., Room 315) 
3:45pm  4:30pm 
Carlos CastilloChavez (Memorial Bldg., Room 315) 
4:45pm  5:30pm 
Juan Gutierrez (Memorial Bldg., Room 315) 
Plenary and Special Public Lectures
Denis Auroux, University of California at Berkeley, USA
An Invitation to Homological Mirror Symmetry
We will give a gentle introduction to some recent developments in the area of mirror symmetry, focusing on two key conjectures in the field: Kontsevich's homological mirror symmetry (1994), which relates
the Fukaya category of a symplectic manifold to the derived category of coherent sheaves of a mirror space, and the StromingerYauZaslow (SYZ) conjecture (1996), which gives a geometric underpinning for the construction of
mirror spaces. We will use simple examples to illustrate these conjectures and their extension beyond the CalabiYau setting in which they were first formulated. Specifically, we will focus on two onedimensional examples, the
cylinder and the pair of pants, to give a flavor of the geometric concepts involved in a general formulation of homological mirror symmetry.
Michael Eichmair, University of Vienna, Austria
On Scalar Curvature, Minimal Surfaces, and the Isoperimetric Problem in the Large
Mark Lewis, University of Alberta, Canada
Population Dynamics in Moving Environments
Classical population dynamics problems assume constant unchanging environments. However, realistic environments fluctuate in both space and time. My lectures will focus on the analysis of population
dynamics in environments that shift spatially, due either to advective flow (eg., river population dynamics) or to changing environmental conditions (eg., climate change). The emphasis will be on the analysis of nonlinear
advectiondiffusionreaction equations in the case where there is strong advection and environments are heterogeneous. I will use methods of spreading speed analysis, net reproductive rate and inside dynamics to understand
qualitative outcomes. Applications will be made to river populations in one and twodimensions and to the genetic structure of populations subject to climate change.
Victor Reiner, University of Minnesota, USA
Finite Reflection Groups and General Linear Groups
We discuss some remarkable counting formulas over finite fields that have arisen in recent years, coming from thinking of finite general linear groups as reflection groups, and pursing their analogy to Weyl
groups.
Yuri Tschinkel, New York University and Simons Institute, USA
Building Institutes
I will discuss the role of foundations in the creation of mathematical centers.
Algebraic Geometry and Topology
Lino Grama, Universidade Estadual de Campinas, Brazil
On the Construction of LG Models on Coadjoint Orbits
In this talk we describe the LG models associated to coadjoint orbits of complex simple Lie groups. We also discuss its FukayaSeidel category in low dimensional examples as well as geometric information
about the mirror manifold.
Andrew Harder, University of Miami, USA
Pseudolattices, del Pezzo Surfaces, and Elliptic Fibrations
I will explore the relationship between factorizations of certain elements in SL2(Z), elliptic fibrations over the disc, and del Pezzo surfaces. It turns out that all three of these things can be modelled
linear algebraically by objects called pseudolattices, and this fact implies us that their classifications are closely related. Finally, I will explain how this can be seen as a manifestation of homological mirror
symmetry.
Paul Horja, University of Miami, USA
Toric Schobers and Dmodules
Many classical mirror symmetry results can be recast using the recent language of perverse sheaves of categories and schobers. In this context, I will explain a RiemannHilbert type conjectural connection
with the Dmodules naturally appearing in mirror symmetry. This is joint work with Ludmil Katzarkov.
Gabriel Kerr, Kansas State University, USA
Spheres in Complex Hypersurfaces
Given a hypersurface X of the complex torus, mirror symmetry predicts a quasiequivalence between the Fukaya category F(X) of X and a certain category of graded matrix factorizations MF (W) on a toric
CalabiYau variety. In this talk, I will describe this correspondence, as well as how it fits in the larger picture of homological mirror symmetry. Exploring the algebraic side, one finds there are many spherical objects in MF
(W) which have combinatorial descriptions. Using phase tropical varieties, I will provide a prediction of the topological mirrors to these objects in F(X) and discuss some generalizations. This is based on joint work with Ilia
Zharkov.
Ernesto Lupercio, Cinvestav, México
SelfOrganized Critical Complex Systems and Algebraic Geometry in the Tropical Limit
In this talk I will survey our recent work relating the mathematics of complex systems and power laws and the tropical geometry of curves in toric manifolds. Collaborators on this project include N.
Kalinin, A. Guzman, Y. Prieto, M. Shkonivkov, V. Kalinina, L. Katzarkov, L. Meersseman, and A. Verjovsky.
Jacob Mostovoy, Cinvestav, México
The Pure Braid Group and the Pure Cactus Group
The topology of the real part of the moduli space of stable curves of genus zero with n marked points is known to be determined completely by its fundamental group, known as the pure cactus group. In this
talk I will describe the analogy between the pure cactus group and the pure braid group and show how it leads to an elementary proof of the residual nilpotency of the pure cactus group, conjectured by Etingof et al.
Manuel Rivera, University of Miami, USA, and Cinvestav, México
Higher Categories, Loop Spaces, and Local Systems
I will describe how basic results of the "brave new homotopy theory" a la Lurie may be applied to improve classical results. More precisely, I will explain how unraveling the combinatorics behind
the "rigidification functor" of Lurie (the left adjoint of the homotopy coherent nerve functor) leads to the improvement of a classical result of Adams which relates the based loop space on a space and the algebraic cobar
construction. Then I will explain the following applications: 1) we obtain algebraic models for different types of path spaces of connected (possibly nonsimply connected) spaces, 2) our results lead to a transparent and
concrete approach to the homotopy theory of (infinity) local systems, 3) we may deduce that the singular chains on a space with its natural algebraic structure, under a notion of weak equivalence stronger than quasiisomorphism,
encodes the fundamental group.
Andrei Teleman, AixMarseilles Université, France
New Methods in the Classification of Class VII Surfaces
Bernardo Uribe, Universidad del Norte, Colombia
The Evenness Conjecture on Equivariant Unitary Bordism
The evenness conjecture for the equivariant unitary bordism groups states that these bordism groups are free modules over the unitary bordism ring in even dimensional generators. In this talk I
will review the cases where the conjecture is known to hold and I will highlight the properties that permit one to prove the conjecture in these cases.
Combinatorics
Marcelo Aguiar, Cornell University, USA
Topics in Hyperplane Arrangements
We will discuss a number of geometric and algebraic constructions associated to real hyperplane arrangements, focusing on the monoid of faces and the category of lunes of the arrangement. Basics on
hyperplane arrangements will be reviewed. We will then discuss the beginnings of a theory of noncommutative Mobius functions and its connections to the structure of the algebra of faces. We will also discuss an extension of a
theorem of Joyal, Klyachko and Stanley relating the homology of the partition lattice to free Lie algebras. These topics are from recent and ongoing joint work with Swapneel Mahajan.
Carolina Benedetti, Universidad de Los Andes, Colombia
A MurnaghanNakayama Rule for Quantum Cohomology of the Flag Manifold
In this talk, we provide a combinatorial rule for the product of a quantum powersum by a quantum Schubert polynomial. This expansion is known, in the classical setting as MurnaghanNakayama rule. Our
expansion involves chains and intervals in the quantum Bruhat order, and cyclic shifts of those. In geometry, a MurnaghanNakayama formula computes the intersection of Schubert cycles with tautological classes coming from the
Chern character.
Sara Billey, University of Washington, USA
Boolean Product Polynomials and SchurPositivity
We study a family of symmetric polynomials that we refer to as the Boolean product polynomials. The motivation for studying these polynomials stems from the computation of the characteristic polynomial of
the real matroid spanned by the nonzero vectors in R^{n} all of whose coordinates are either 0 or 1. To this end, one approach is to compute the zeros of the Boolean product polynomials over finite fields. The zero loci
of these polynomials cut out hyperplane arrangements known as resonance arrangements, which show up in the context of double Hurwitz polynomials. By relating the Boolean product polynomials to certain total Chern classes of
vector bundles, we establish their Schurpositivity by appealing to a result of Pragacz relying on earlier work on numerical positivity by FultonLazarsfeld. Subsequently, we study a twoalphabet version of these polynomials
from the viewpoint of Schurpositivity. As a special case of these polynomials, we recover symmetric functions first studied by Desarmenien and Wachs in the context of descents in derangements.
This is based on joint work with Lou Billera and Vasu Tewari.
Rafael González D'León, Universidad Sergio Arboleda, Colombia
The Whitney Duals of a Graded Poset
Two posets are Whitney duals to each other if the (absolute value of their) Whitney numbers of the first and second kind are switched between the two posets. We introduce new types of edge and chainedge
labelings of a graded poset which we call Whitney labelings. We prove that every graded poset with a Whitney labeling has a Whitney dual and we show how to explicitly construct a Whitney dual using a technique that involves
quotient posets. As an application of our main theorem, we show that geometric lattices, the lattice of noncrossing partitions, the poset of weighted partitions studied by González D'LeónWachs and the
R*Slabelable posets studied by SimionStanley all have Whitney duals. We also show that a graded poset P with a Whitney labeling admits a local action of the 0Hecke algebra on the set of maximal chains of P. The characteristic
of the associated representation is Ehrenborg's flag quasisymmetric function of P. This is joint work with Josh Hallam (Wake Forest University).
Patricia Hersh, North Carolina State University, USA
Topology and Combinatorics of Totally Nonnegative Spaces
We will discuss results, both old and new, regarding the topological and combinatorial structure of totally nonnegative varieties. Interest in these varieties comes from geometric representation theory and
from the theory of cluster algebras. In many cases, these varieties arise as images of quite interesting maps, with the fibers of these maps describing relations for instance amongst exponentiated Chevalley generators. We will
discuss not only the structure of some of these spaces themselves but also of these fibers. Parts of this are joint work with James Davis and Ezra Miller and with Drew Armstrong.
Alejandro Morales, University of Massachusetts Amherst, USA
Hook Formulas for Skew Shapes
The celebrated hooklength formula of Frame, Robinson and Thrall from 1954 gives a product formula for the number of standard Young tableaux of straight shape. No such product formula exists for general
skew shapes, though there are determinantal formulas or positive formulas involving LittlewoodRichardson coefficients. In 2014, Naruse announced a new positive formula coming from geometry that is very close to the formula for
straight shapes and has spurred new interest in tableaux enumeration. I will talk about this formula and how it has led to new results about semistandard tableaux and reverse plane partitions, asymptotics of the number of
standard tableaux, and new product formulas for the number of tableaux of certain skew shapes. This is joint work with Igor Pak and Greta Panova.
José Alejandro Samper Casas, University of Miami, USA
Matroid Independence Complexes with Prescribed Homotopy Type
It is well known that the independence complex of any matroid without coloops is homotopy equivalent to a wedge of k > 0 equidimensional spheres. We prove that if the dimension and the number of
spheres is fixed, then only finitely many such independence complexes exist. This counterintuitive property leads to new structural questions such as upper and lower bound theorems/conjectures for matroids based on the two
parameters mentioned. New theorems about the face numbers of the independence complex also show up. If time permits we will discuss similar results for geometric lattices. This is joint work with F. Castillo.
John Shareshian, Washington University, USA
Regular Hessenberg Varieties and Characters of Hecke Algebras
Combining results of BrosnanChow and ClearmanHyattSheltonSkandera, one sees that Poincaré polynomials of type A regular Hessenberg varieties give values of parabolic characters of the type A
Hecke algebras evaluated at certain KazhdanLusztig basis elements. I will describe joint work with Ryan Schneider, along with work of Alex Woo, in which it is shown that, although the corresponding result does not always hold
in all Lie types, it does hold in many cases.
Stephanie van Willigenburg, University of British Columbia, Canada
The ePositivity of Chromatic Symmetric Functions
The chromatic polynomial was generalized to the chromatic symmetric function by Stanley in his seminal 1995 paper. This function is currently experiencing a flourishing renaissance, in particular the study
of the positivity of chromatic symmetric functions when expanded into the basis of elementary symmetric functions, that is, epositivity.
In this talk we approach the question of epositivity from various angles. Most pertinently we resolve the 1995 statement of Stanley that no known graph exists that is not contractible to the claw, and whose chromatic symmetric
function is not epositive.
This is joint work with Soojin Cho, Samantha Dahlberg and Angele Foley, and no prior knowledge is assumed.
Differential Geometry and Geometric Analysis
Lucas Ambrozio, University of Warwick, UK
Free Boundary Minimal Surfaces
In recent years, the theory of free boundary minimal surfaces, that is, of critical points of the area functional on the space of surfaces whose boundaries are contained inside the boundary of the ambient
manifold, has been developing fast into several directions: construction of new examples by several methods (e.g. maximisation of Steklov eigenvalues), classifications theorems, index estimates, compactness results. In this talk
we will present an overview of some of these recent developments.
Otis Chodosh, Princeton University, USA
Minimal Surfaces and the AllenCahn Equation on 3 Manifolds, Part II
We will describe recent work on the AllenCahn semilinear PDE on 3 manifolds including curvature, multiplicity, and index estimates.
Robert Haslhofer, University of Toronto, Canada
Minimal TwoSpheres in ThreeSpheres
We prove that any manifold diffeomorphic to S^{3} and endowed with a generic metric contains at least two embedded minimal twospheres. The existence of at least one minimal twosphere was
obtained by SimonSmith in 1983. Our approach combines ideas from minmax theory and mean curvature flow. We also establish the existence of smooth mean convex foliations in threemanifolds. Finally, we apply our methods to
solve a problem posed by S.T. Yau in 1987, and to show that the assumptions in the multiplicity one conjecture and the equidistribution of widths conjecture are in a certain sense sharp. This is joint work with Dan
Ketover.
Chao Li, Stanford University and Princeton Unversity, USA
A Polyhedron Comparison Theorem in Positive Scalar Curvature
We establish a comparison theorem for polyhedra in manifolds with nonnegative scalar curvature, answering affirmatively a dihedral rigidity conjecture by Gromov. For a large collection of polyhedra with
interior nonnegative scalar curvature and mean convex faces, we prove the dihedral angles along its edges cannot be everywhere less or equal than those of the corresponding Euclidean model, unless it is a isometric to a flat
polyhedron. We will start the discussion from 3manifolds, and illustrate how our result is parallel to the positive mass theorem, and thus generalizable to higher dimensions.
Siyuan Lu, Rutgers University, USA
Isometric Embedding: Old and New
In this talk, we will first review the classic Weyl's isometric embedding theorem, solved by Nirenberg and Pogorelov. A key part of the proof is to derive the mean curvature estimate. We will discuss two
different approaches for the curvature estimate: global estimate and interior estimate. We will then discuss how to extend these two approaches to general ambient space. If time permits, we will further discuss Weyl's
embedding theorem in general Riemannian manifolds and its applications in general relativity.
Christos Mantoulidis, Massachusetts Institute of Technology
Minimal Surfaces and the AllenCahn Equation on 3 Manifolds, Part I
We will describe recent work on the AllenCahn semilinear PDE on 3 manifolds including curvature, multiplicity, and index estimates.
Abraão Mendes, Universidade Federal de Alagoas, Brazil
Rigidity of Free Boundary Surfaces
Martín Reiris, Universidad de la RepúblicaMontevideo, Uruguay
New Techniques a la BakryEmery on Vacuum Static and Stationary Solutions
The classification of static and stationary solutions of the Einstein equations is one of the oldest and most natural problems in General Relativity. The celebrated uniqueness theorem of the Schwarzschild
solutions (Israel, Robinson et al, Bunting/MasoodulAlam) classifies all asymptotically flat (3+1) static vacuum black holes. Recently, comparison techniques a la BakryEmery have been applied to shown that, without any
asymptotic assumption, vacuum static black holes are either (i) Schwarzschild, (ii) Boosts, or (iii) of Myers/KorotkinNicolai type, namely their topology is that of a solid threetorus minus a finite number of open threeballs
and the asymptotic is Kasner, (see arXiv:1806.00818 arXiv:1806.00819). I will discuss how BakryEmery techniques could be used to shed light in the still open problem of the existence of vacuum stationary (rotating) black holes
of Myers/KorotkinNicolai type. Achieving this goal would be a step towards the classification of vacuum stationary black holes, still an unresolved problem.
Lu Wang, University of Wisconsin, USA
SelfSimilar Solutions of Mean Curvature Flow
Mean curvature flow is the negative gradient flow of the volume functional, which decreases the volume of hypersurfaces in the steepest way. The flow starting from any compact hypersurface will develop
singularities in finite time. Selfsimilar solutions of mean curvature flow play an important role in understanding the asymptotic behavior of the flow near singularities. In this talk, I will survey some known results as well
as some open problems about selfsimilar solutions of mean curvature flow – with a particular emphasis on properties of selfshrinking solutions.
Mathematical Biology
Carlos CastilloChavez, Arizona State University, USA and Yachay University of Experimental Technical Research, Ecuador
Scaling Up the Impact of Dynamic Individual Decisions in Response to Ongoing Epidemic Outbreaks
The long standing challenge posed by the threat of emergent or reemergent diseases is intimately linked to the use that individuals make of disease risk information. A modeling framework that accounts for
the impact that an ongoing disease outbreak has on the decisions that individuals make based on their real or perceived risk of infection is revisited.
Recent work with collaborators at various
institutions including Eli Fenichel, Charles Perrings and Ben Morin is highlighted. The research is based on a behavioral framework where individual decisions are based on the tradeoffs made in response to costs associated with
the present or future risk of infection and the potential loss of benefits that may result as a consequence of risk aversion decisions – risks due in part to changes in prevalence. This research project will be highlighted
in the context of influenza.
Juan Gutierrez, University of Georgia, USA
The Math of MultiScaling: From Molecular Dynamics to Epidemiological Processes of Malaria
The advent of highthroughput molecular technologies in particular, and the broad availability of data, in general, have forced the quantitative biology community to rethink how to conceive, build, and
validate mathematical models. In this talk I will demonstrate how molecular and cellular processes are related to the epidemiology of malaria. We will explore (i) asymptomaticity at the epidemiological level, (ii) the cellular
models that explain this phenomenon as an interaction between the immune system and infected red blood cells, (iii) mathematical models that link cellular and transcriptional time series, (iv) transcriptomic analysis, and
finally (vi) highthroughput insilico drug discovery to solve an epidemiological problem. All these linked analyses provide a comprehensive picture that no single scale can produce alone. The usefulness of models under this
light takes on new meanings, and this broad scope requires the cooperation of scientists coming from very different intellectual traditions. In this talk we will also explore how an information system that delivers Adaptive
Learning for Interdisciplinary Collaborative Environments (ALICE) is used to train scientists in this new normal.
Xi Huo, University of Miami, USA
Modelling the Antibiotic Use in Intensive Care Units – Comparing Deescalation and Continuation
Antimicrobial deescalation refers to the treatment mechanism of switching from empiric antibiotics with good coverage to alternatives based on laboratory susceptibility test results, with the aims of
reducing costs and avoiding unnecessary use of broadspectrum antibiotics. Though widely practiced and recommended, the benefits and tradeoffs of this strategy have not been well understood. In this talk, we will first show our
preliminary simulation results of a set of multistrainmultidrug models in an intensive care unit setting, to numerically compare deescalation with the conventional strategy called antimicrobial continuation. Then we simplify
the previous models to compare the longterm dynamical behaviors between deescalation and continuation systems under a doublestraindoubledrug scenario. Finally we extend our models to seek for optimal antibiotic use
strategies under a triplestraintripledrug scenario. The major conclusion of this study shows that, if we suppose there are two identical intensive care units that separately adopt deescalation and continuation as the major
drug use strategy, then the one following deescalation: (1) could maintain either higher or lower percentage of colonized patients in the twostrain transmission scenario; (2) is superior in preventing outbreaks of strains
resistant to the empiric antibiotic.
KingYeung Lam, Ohio State University, USA
Invasion of Open Space by Two Competing Species
I will discuss a question raised by Shigesada and Kawasaki in Chapter 7 of their monograph, concerning the spreading properties of two competing species on the real line when the initial values are null or
exponentially decaying in a right halfline. In the case of compactly supported initial values, we prove that the first species spreads with the KPP speed of the single species, whereas the speed of the second species can be
given by an exact formula depending on the speed of the first species. This is joint work with Leo Girardin (Paris VI). If time allows, I will also talk about some recent progress obtained with Qian Liu (OSU and Renmin Univ. of
China).
Suzanne Lenhart, University of Tennessee, USA
Optimal control techniques for management strategies in biological models
Two examples with different optimal control techniques to choose management actions will be presented. One model is a PDE system representing Zika spreading across a state in Brazil; the control varying in
space and time is a vaccination rate. Data from Brazil were used to estimate parameters. The second model represents a large scale forest fire. We incorporate the stochasticity of the time of a fire into our model and explore
the tradeoffs between prevention management spending and suppression spending. A large fire event in the past was used to form an illustrative example.
Salomé Martínez, Universidad de Chile, Chile
Multiple Steady States for a Competition System Supporting an IdealFree Distribution
Nancy Rodriguez, University of North Carolina, USA
BirthJump Processes in Plant Dynamics
In this talk I will introduce a model for the dynamics of the growth and dispersal of plants in various environments. The discrete model is based on a birthjump process which exhibits wavelike solutions.
After discussing the continuum limit, which is an nonlocal reactiondiffusion equation, I will present the proof of existence of traveling waves for speeds above a critical threshold (both sharp and continuously differentiable)
in the diffusionlimit assuming a logarithmictype growth term. I will conclude by verifying the theoretical results presented via the use of numerical simulations.
Zhisheng Shuai, University of Central Florida, USA
Biased population movement and infectious disease dynamics
Many recent outbreaks and spatial spread of infectious diseases have been influenced by human movement over air, sea and land transport networks, and/or anthropogenicinduced pathogen/vector movement. These
spatial movements in heterogeneous environments and networks are often asymmetric (biased). The effects of asymmetric movement versus symmetric movement will be investigated using several epidemiological models from the
literature. These investigations provide a better understanding of disease transmission and control in the real life application.
Jorge VelascoHernandez, Universidad Nacional Autónoma de México, México
Dengue Dynamics in Southern Mexico: An Approximation to its Population Dynamics and the Role of Population Movement
We present data and analysis of dengue incidence in several states of Mexico. A metapopulation model is presented along with further commentaries on the construction of a dengue network for mobility in
these regions.