Print Friendly printer friendly
 Events
Shen-Ning Tung
Universität Duisburg-Essen
Thu 1 Mar 2018, 3:30pm
Number Theory Seminar
Math 126
On the automorphy of 2-dimensional potentially semistable deformation rings of \GQp
Math 126
Thu 1 Mar 2018, 3:30pm-4:30pm

Abstract

Using p-adic local Langlands correspondence for GL2(Qp), we prove that the support of patched modules constructed by Caraiani, Emerton, Gee, Geraghty, Paskunas, and Shin meet every irreducible component of the potentially semistable deformation ring. This gives a new proof of the Breuil-Mézard conjecture for 2-dimensional representations of the absolute Galois group of Qp when p > 2, which is new in the case p = 3 and \bar{r} a twist of an extension of the trivial character by the mod p cyclotomic character. As a consequence, a local restriction in the proof of Fontaine-Mazur conjecture by Kisin is removed.
hide
Alperen Bulut
UBC
Fri 2 Mar 2018, 12:00pm
Graduate Student Seminar
MATH 225
Axioms, Sets, and some Logic
MATH 225
Fri 2 Mar 2018, 12:00pm-1:00pm

Abstract

Most of the contemporary mathematics we use is built on set theory. To avoid any possible complications, the axioms describing such a system have to be as precise as possible. As a pedantic person who tries to pay attention to logical details (since I find it difficult to trust even my own judgement), I will discuss about various topics and situations which I feel many of us should handle more delicately. Then I will use this opportunity as a segue to talk about axioms, set theory, functions, and some logic.
hide
SNS, Pisa
Fri 2 Mar 2018, 3:00pm SPECIAL
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium--Some specialization problems in Geometry and Number Theory
ESB 2012
Fri 2 Mar 2018, 3:00pm-4:00pm

Abstract

We shall survey over the general issue of
`specializations which preserve a property',
for a parametrized family of algebraic varieties.
We shall limit ourselves to a few examples.
We shall start by recalling typical contexts like
Bertini and Hilbert Irreducibility theorems,
illustrating some new result.
Then we shall jump to much more recent instances,
related to algebraic families of abelian varieties.

Note for Attendees

Refreshments will be served in ESB 4133 from 2:45 p.m.-3:00 p.m.
hide
Université Laval
Mon 5 Mar 2018, 11:00am SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Introduction to Supersingular Iwasawa Theory of Elliptic Curves (talk 1)
ESB 4127
Mon 5 Mar 2018, 11:00am-12:00pm

Abstract

Let E/Q be an elliptic curve. In Iwasawa Theory, we study the behaviours of E over a tower of number fields. For example, it is known that the Mordell Weil ranks of E over all p-power cyclotomic extensions of Q are bounded when p does not divide the conductor of E. Surprisingly, the techniques required to show this are very different depending on the number of points on the finite curve when we consider E reduced modulo p. The easier case is when E has "ordinary" reduction at p and the more difficult case is when E has "supersingular" reduction at p. I will review the Iwasawa-theoretic tools used to study the behaviours of E over cyclotomic fields in these two cases. I will also discuss some recent developments on the Iwasawa theory of elliptic curves over quadratic extensions of Q.

This is talk 1 of 3 by the speaker, and part of the PIMS Thematic Events on "Galois groups in arithmetic".
hide
University of Washington
Mon 5 Mar 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126
Quotients of algebraic varieties
MATH 126
Mon 5 Mar 2018, 4:00pm-5:00pm

Abstract

In this talk, we will address the following question:  given an algebraic group G acting on a variety X, when does the quotient X/G exist?  We will provide an answer to this question in the case that G is reductive by giving necessary and sufficient conditions for the quotient to exist.  We will discuss various applications to equivariant geometry, moduli problems and Bridgeland stability.
hide
Bernie Shizgal
Department of Chemistry, UBC
Tue 6 Mar 2018, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Pseudospectral Methods with Nonclassical Quadratures
ESB 4133 (PIMS Lounge)
Tue 6 Mar 2018, 12:30pm-1:30pm

Abstract

A spectral method for the solution of integral and differential equations is generally understood to be an expansion of the solution in a Fourier series. Chebyshev polynomials are also often the preferred basis set for many problems. In kinetic theory, the Sonine polynomials have been used for decades for the solution of the Boltzmann equation and the calculation of transport coefficients. This talk will focus on the use of nonclassical polynomials orthonormal with respect to an appropriate weight function chosen dependent on the problem considered. The associated quadrature rules are also used in the pseudospectral solution of several different problems in kinetic theory and quantum mechanics. The recurrence coefficients in the three term recurrence relation for the nonclassical polynomials define the Jacobi matrix, J, and are determined numerically with the Gautschi-Stieltjes procedure. The quadrature points are the eigenvalues of J and the weights are the first components of the i th eigenfunction. This methodology is applied to the solution of the Fokker-Planck equation(1), the Schroedinger equation (2), the evaluation of integrals in quantum chemistry (3) and for nuclear reaction rate coefficients (4).

(1) Pseudospectral solution of the Fokker-Planck equation: the eigenvalue spectrum and the approach to equilibirum. J. Stat. Phys. 164, 1379-1393 (2016).
(2) Pseudospectral method of solution of the Schroedinger equation with nonclassical polynomials; the Morse and Poschl-Teller (SUSY) potentials. J. Comput. Theor. Chem. 1084, 51-58 (2016).
(3) A novel Rys quadrature algorithm for use in the calculation of electron repulsion integrals. J. Comput. Theor. Chem. 1074, 178-184 (2015).
(4) An efficient nonclassical quadrature for the calculation of nonresonant nuclear fusion reaction rate coefficients from cross section data. Comp. Phys. Comm. 205, 61-69 (2016). 
hide
McGill
Tue 6 Mar 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Blowing-up solutions for critical elliptic equations on a closed manifold
ESB 2012
Tue 6 Mar 2018, 3:30pm-4:30pm

Abstract

In this talk, we will look at the question of existence of blowing-up solutions for smooth perturbations of energy-critical elliptic nonlinear Schrödinger equations on a closed manifold. From a result of Olivier Druet, we know that in dimensions different from 3 and 6, a necessary condition for the existence of blowing-up solutions with bounded energy is that the linear part of the limit equation agrees with the conformal Laplacian at least at one blow-up point. I will present new existence results in situations where the limit equation is different from the Yamabe equation away from the blow-up point. I will also discuss the special role played by the dimension 6. This is a joint work with Frederic Robert.
hide
Harvard University.
Tue 6 Mar 2018, 4:00pm
Discrete Math Seminar
ESB 4127
On incidences between points and unit circles in R^3 and related questions
ESB 4127
Tue 6 Mar 2018, 4:00pm-5:00pm

Abstract

In this talk I will survey results related to incidences between points and algebraic curves in dimensions 2,3 and 4, and will concentrate on the problem of incidences between points and restricted families of curves in R^3, e.g, "unit circles" is a restricted family inside the family of circles in R^3. I will show a new upper bound for incidences between points and unit circles in R^3, and state more general results and other applications as well.
hide
Université Laval
Wed 7 Mar 2018, 11:00am SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Introduction to Supersingular Iwasawa Theory of Elliptic Curves (talk 2)
ESB 4127
Wed 7 Mar 2018, 11:00am-12:00pm

Abstract

Let E/Q be an elliptic curve. In Iwasawa Theory, we study the behaviours of E over a tower of number fields. For example, it is known that the Mordell Weil ranks of E over all p-power cyclotomic extensions of Q are bounded when p does not divide the conductor of E. Surprisingly, the techniques required to show this are very different depending on the number of points on the finite curve when we consider E reduced modulo p. The easier case is when E has "ordinary" reduction at p and the more difficult case is when E has "supersingular" reduction at p. I will review the Iwasawa-theoretic tools used to study the behaviours of E over cyclotomic fields in these two cases. I will also discuss some recent developments on the Iwasawa theory of elliptic curves over quadratic extensions of Q.

This is talk 2 of 3 by the speaker, and part of the PIMS Thematic Events on "Galois groups in arithmetic".
hide
UBC
Wed 7 Mar 2018, 3:10pm
Probability Seminar
LSK 460
The boundary of the zero set and boundary local time of one-dimensional super-Brownian motion
LSK 460
Wed 7 Mar 2018, 3:10pm-4:10pm

Abstract

Super-Brownian motion is a measure-valued Markov process which arises as the scaling limit of several discrete models, including branching random walk. In dimension one, it has a continuous density. In this talk I will discuss the construction of a boundary local time for the density, which is a random measure supported on the boundary of its zero set. I will then show how a close analysis of the right endpoint of the density's support is used to prove that the local time is positive almost surely (when the process itself is non-zero). An application energy method using the local time then gives an almost sure characterization of the Hausdorff dimension of the boundary of the zero set, completing a result which was previously only known to hold with positive probability.

This talk includes joint work with Ed Perkins.
hide
Harvey Mudd College
Wed 7 Mar 2018, 3:15pm
Mathematical Biology Seminar
ESB 4127
Agent-Based and Continuous Models of Locust Hopper Bands: The Role of Intermittent Motion, Alignment and Attraction
ESB 4127
Wed 7 Mar 2018, 3:15pm-4:15pm

Abstract

Locust swarms pose a major threat to agriculture, notably in North Africa and the Middle East. In the early stages of aggregation, locusts form hopper bands. These are coordinated groups that march in columnar structures that are often kilometers long and may contain millions of individuals. We propose a model for the formation of locust hopper bands that incorporates intermittent motion, alignment with neighbors, and social attraction, all behaviors that have been validated in experiments. Using a particle-in-cell computational method, we simulate swarms of up to a million individuals, which is several orders of magnitude larger than what has previously appeared in the locust modeling literature. We observe hopper bands in this model forming as a fingering instability. Our model also allows homogenization to yield a system of partial integro-differential evolution equations. We identify a bifurcation from a uniform marching state to columnar structures, suggestive of the formation of hopper bands.
hide
Université Laval
Fri 9 Mar 2018, 11:00am SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Introduction to Supersingular Iwasawa Theory of Elliptic Curves (talk 3)
ESB 4127
Fri 9 Mar 2018, 11:00am-12:00pm

Abstract

Let E/Q be an elliptic curve. In Iwasawa Theory, we study the behaviours of E over a tower of number fields. For example, it is known that the Mordell Weil ranks of E over all p-power cyclotomic extensions of Q are bounded when p does not divide the conductor of E. Surprisingly, the techniques required to show this are very different depending on the number of points on the finite curve when we consider E reduced modulo p. The easier case is when E has "ordinary" reduction at p and the more difficult case is when E has "supersingular" reduction at p. I will review the Iwasawa-theoretic tools used to study the behaviours of E over cyclotomic fields in these two cases. I will also discuss some recent developments on the Iwasawa theory of elliptic curves over quadratic extensions of Q.

This is talk 3 of 3 by the speaker, and part of the PIMS Thematic Events on "Galois groups in arithmetic".
hide
UBC Math
Fri 9 Mar 2018, 3:00pm
Department Colloquium
ESB 2012
Graduate Research Award: Enumerative Geometry, Hurwtiz Numbers and Beyond
ESB 2012
Fri 9 Mar 2018, 3:00pm-4:00pm

Abstract

Enumerative geometry studies the enumeration of geometric structures, however there are also strong links to many other areas of mathematics. A quintessential example of this is the study of Hurwitz numbers which dates back to the 19th century. Using Hurwitz numbers I will explicitly describe links between geometry, combinatorics, representation theory and physics. I will then discuss recent progress in the subject using modern techniques.

Note for Attendees

Refreshments will be served in ESB 4133 from 2:45 p.m.-3:00 p.m.
hide
Edmonton
Mon 12 Mar 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126
On generic flag varieties of Spin(11) and Spin(12)
MATH 126
Mon 12 Mar 2018, 4:00pm-5:00pm

Abstract

Let X be the variety of Borel subgroups of a split semisimple algebraic group G over a field, twisted by a generic G-torsor. Conjecturally, the canonical epimorphism of the Chow ring CH(X) onto the associated graded ring GK(X) of the topological filtration on the Grothendieck ring K(X) is an isomorphism. We prove new cases G=Spin(11) and G=Spin(12) of this conjecture. On  an equivalent note, we compute the Chow ring CH(Y) of the highest orthogonal grassmannian Y for the generic 11- and 12-dimensional quadratic forms of trivial discriminant and Clifford invariant. In particular,  we describe the torsion subgroup of the Chow group CH(Y) and determine its order which is  equal to 16 777 216. On the other hand, we show that the Chow group of 0-cycles on Y is torsion-free.
hide
Maurice Queyranne
Operations and Logistics Division, Sauder School of Business, UBC
Tue 13 Mar 2018, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Optimal pits and optimal transportation
ESB 4133 (PIMS Lounge)
Tue 13 Mar 2018, 12:30pm-1:30pm

Abstract

In open pit mining, one must dig a pit, that is, excavate upper layers of ground to reach valuable minerals. The walls of the pit must satisfy some geomechanical constraints (maximum slope constraints) so as not to collapse. The _ultimate pit limits _problem is to determine an optimal pit, the total volume to be extracted so as to maximize total net profits. We set up the problem in a continuous space framework (as opposed to discretized space, such as with block models), and we show, under weak assumptions, the existence of an optimum pit. For this, we formulate an infinite-dimensional, optimal transportation problem of the Kantorovich type, where the cost function is lower semi-continuous and is allowed to take the value +infinity. We show that this transportation problem is a strong dual to the optimum pit problem, and also yields optimality (complementary slackness) conditions. This approach has the potential of leading to novel algorithmic approaches, yet to be explored, to the ultimate pit limits and related mine planning problems.

This is joint work with Ivar Ekeland (CEREMADE, Université Paris-Dauphine).
hide
Hebrew University
Wed 14 Mar 2018, 2:00pm
Number Theory Seminar
Math 126
Analytic torsion for congruence quotients of SL(n,R)/SO(n)
Math 126
Wed 14 Mar 2018, 2:00pm-3:00pm

Abstract

Analytic torsion is a classical invariant for compact Riemannian manifolds. The Cheeger-Mueller Theorem relates it to its combinatorial equivalent, the Reidemeister torsion. This can be exploited to study the torsion homology of certain arithmetic lattices as in recent work of Bergeron and Venkatesh.

In my talk I want to explain the definition of analytic torsion for congruence quotients of X=SL(n,R)/SO(n) (which are non-compact). Further, I want to discuss the behavior of the analytic torsion  in the limit N->infinity for the spaces G(N)\X with G(N) the principal congruence subgroup of level N in SL(n, R). (Joint work with W. Mueller.)
hide
University of Washington
Wed 14 Mar 2018, 3:10pm
Probability Seminar
LSK 460
Multiplicative Schrödinger problem and the Dirichlet transport
LSK 460
Wed 14 Mar 2018, 3:10pm-4:10pm

Abstract

 
We consider a Monge-Kantorovich optimal transport problem on the unit simplex with a cost function given by the log of the Euclidean inner product. We show that the transport is the large deviation limit of multiplication by the Dirichlet (or, gamma) process and suitable normalization. This is a multiplicative counterpart to the Wasserstein-2 transport that is carried by adding Brownian motion to an initial mass distribution (called the Schrödinger problem by Léonard). The potential function and the Lagrangian of this transport appear to be closely related to the Wasserstein diffusion (Brownian motion on the Wasserstein space) put forward by Sturm and other coauthors, although it is unclear what the exact nature of this relationship is.
hide
Notre Dame University
Wed 14 Mar 2018, 3:15pm
Mathematical Biology Seminar
ESB 4127
Modeling the Dynamics of Cdc42 Oscillation in Fission Yeast
ESB 4127
Wed 14 Mar 2018, 3:15pm-4:15pm

Abstract

We present a mathematical model of the core mechanism responsible for the regulation of polarized growth dynamics by the small GTPase Cdc42. The model is based on the competition of growth zones of Cdc42 localized at the cell tips for a common substrate (inactive Cdc42) that diffuses in the cytosol. We consider several potential ways of implementing negative feedback between Cd42 and its GEF in this model that would be consistent with the observed oscillations of Cdc42 in fission yeast. We analyze the bifurcations in this model as the cell length increases, and total amount of Cdc42 and GEF increase. Symmetric antiphase oscillations at two tips emerge via saddle-homoclinic bifurcations or Hopf bifurcations. We find that a stable oscillation and a stable steady state can coexist, which is consistent with the experimental finding that only 50% of bipolar cells oscillate. Our model suggests that negative feedback is more likely to be acting through inhibition of GEF association rather than upregulation of GEF dissociation.
hide
Concordia University
Thu 15 Mar 2018, 2:00pm SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
p-Adic modular forms (talk 1)
ESB 4127
Thu 15 Mar 2018, 2:00pm-3:30pm

Abstract

p-Adic modular forms have first been defined by J.-P. Serre as q-expansions and have later been interpreted geometrically by N. Katz as sections of certain modular line bundles over the ordinary locus of the relevant modular curves. Katz also defined overconvergent modular forms of integer weights as overconvergent sections of the modular line bundles of that weight. Many years later H. Hida and respectively R. Coleman defined ordinary, respectively finite slope overconvergent modular forms of arbitrary, p-adic weight as q-expansions and using these Coleman and Mazur constructed at the end of the 90's the famous eigencurve. Recently, together with Andreatta, Pilloni and Stevens we have been able to geometrically redefine the overconvergent modular forms of Hida and Coleman and so we were able to generalize these constructions to Hilbert and Siegel modular forms.

This is talk 1 of 2 by the speaker, and part of the PIMS Thematic Events on "Galois groups in arithmetic".
hide
PhD Candidate: Robert Fraser
Mathematics, UBC
Thu 15 Mar 2018, 2:15pm SPECIAL
Room 104, MATH BLDG., 1984 Mathematics Road, UBC
Doctoral Exam: Configurations in Fractal Sets in Euclidean and Non-Archimedean Local Fields
Room 104, MATH BLDG., 1984 Mathematics Road, UBC
Thu 15 Mar 2018, 2:15pm-4:15pm

Details

Abstract: We discuss four different problems. The first, a joint work with Malabika Pramanik, concerns large subsets of \mathbb{R}^n that do not contain various types of configurations. We show that a collection of v points satisfying a continuously differentiable v-variate equation in \mathbb{R} can be avoided by a set of Hausdorff dimension \frac{1}{v-1} and Minkowski dimension 1. The second problem concerns large subsets of vector spaces over non-archimedean local fields that do not contain configurations. Results analogous to the real-variable cases are obtained in this setting. The third problem is the construction of measure-zero Besicovitch-type sets in K^n for non-archimedean local fields K. This construction is based on a Euclidean construction of Wisewell and an earlier construction of Sawyer. The fourth problem, a joint work with Kyle Hambrook, is the construction of an explicit Salem set in \mathbb{Q}_p. This set is based on a Euclidean construction of Kaufman.

Note for Attendees

Latecomers will not be admitted.
hide
Concordia University
Fri 16 Mar 2018, 11:00am SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
p-Adic modular forms (talk 2)
ESB 4127
Fri 16 Mar 2018, 11:00am-12:30pm

Abstract

p-Adic modular forms have first been defined by J.-P. Serre as q-expansions and have later been interpreted geometrically by N. Katz as sections of certain modular line bundles over the ordinary locus of the relevant modular curves. Katz also defined overconvergent modular forms of integer weights as overconvergent sections of the modular line bundles of that weight. Many years later H. Hida and respectively R. Coleman defined ordinary, respectively finite slope overconvergent modular forms of arbitrary, p-adic weight as q-expansions and using these Coleman and Mazur constructed at the end of the 90's the famous eigencurve. Recently, together with Andreatta, Pilloni and Stevens we have been able to geometrically redefine the overconvergent modular forms of Hida and Coleman and so we were able to generalize these constructions to Hilbert and Siegel modular forms.

This is talk 2 of 2 by the speaker, and part of the PIMS Thematic Events on "Galois groups in arithmetic".
hide
UBC Math
Fri 16 Mar 2018, 3:00pm
Department Colloquium
ESB 2012
Graduate Research Award: Multi-Scale Modelling in Cellular Systems
ESB 2012
Fri 16 Mar 2018, 3:00pm-4:00pm

Abstract

Individually and collectively, cells are organized systems with many interacting parts. Mathematical models allow us to infer behaviour at one level of organization from information at another level. In this talk, I will share two biological questions that are answered through the development of new mathematical approaches and novel models.

(1) Molecular motors are responsible for transporting material along molecular tracks (microtubules) in cells. Typically, transport is described by a system of reaction-advection-diffusion partial differential equations (PDEs). To understand how the behaviour of many molecular motors, various model parameters, and nonlinear interactions affect the overall transport process at the cellular level, I develop an asymptotic quasi-steady-state approach, reducing the full PDE system to a single nonlinear PDE. I find that the approximating PDE is a conservation law for the total density of motors within the cell, with effective diffusion and velocity that depend nonlinearly on the motor densities and model parameters.

(2) Protein regulators (GTPases) modulate cell shape and forces exerted by cells. Meanwhile, cells sense forces such as tension. The implications of this two-way feedback on cell behaviour is of interest to biologists. I explore this question by developing a simple mathematical model for GTPase signalling and cell mechanics. The model explains a spectrum of behaviours, including relaxed or contracted cells and cells that oscillate between these extremes. Through bifurcation analysis, I find that changes in single cell behaviour can be explained by the strength of feedback from tension to signalling. When such model cells are connected to one another in a row or in a 2D sheet, waves of contraction/relaxation propagate through the tissue. Model predictions are qualitatively consistent with developmental-biology observations.

This is joint work with Dhananjay Bhaskar, Leah Edelstein-Keshet, Tim Small, and Michael Ward.

Note for Attendees

Refreshments will be served in ESB 4133 from 2:45 p.m.-3:00 p.m.
hide
School of Sustainability, Arizona State
Mon 19 Mar 2018, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
The Challenge of Good Environmental Governance: Insights from a Dynamical Systems Perspective.
ESB 2012
Mon 19 Mar 2018, 3:00pm-4:00pm

Abstract

Environmental governance can be viewed as the process by which a group of individuals builds a set of feedbacks into their social and economic systems to maintain  some set of stable structures that promote wellbeing.  These feedbacks often take the form of institutions, the rules and norms that structure repeated human interactions. An institutional statement such as "if the fishery biomass, forest cover, groundwater level, etc.  is below (above) a certain value, then extraction must (may) be adjusted downward (upward)" can be mathematically formalized as a feedback policy in a dynamical system. As such, dynamical systems theory provides a powerful set of tools to study institutions, governance, and environmental policy. In this talk, I will discuss several dynamic models of social-ecological systems that, when combined with experimental and comparative case-study techniques, can be used to explore the very rich space of environmental governance structures observed in practice, and how they may be used to address the challenge of good environmental governance.

Note for Attendees

Reception beforehand in ESB 4133 (the PIMS lounge). Marty is the distinguished IAM Alumni Lecturer this year. 
hide
Oregon
Mon 19 Mar 2018, 4:00pm SPECIAL
Algebraic Geometry Seminar
MATX 1118
The quantum Hikita conjecture
MATX 1118
Mon 19 Mar 2018, 4:00pm-5:00pm

Abstract

The Hikita conjecture relates the cohomology ring of a symplectic resolution to the coordinate ring of another such resolution. I will explain this conjecture, and present a new version of the conjecture involving the quantum cohomology ring. There will be an emphasis on explicit examples.
hide
University of California, Davis
Tue 20 Mar 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Stability of the superselection sectors of Kitaev’s abelian quantum double models
ESB 2012
Tue 20 Mar 2018, 3:30pm-4:30pm

Abstract

Kitaev’s quantum double models provide a rich class of examples of two-dimensional lattice models with topological order in the ground states and a spectrum described by anyonic elementary excitations. The infinite volume ground states of the abelian quantum double models come in a number of equivalence classes called superselection sectors. We prove that the superselection structure remains unchanged under uniformly small perturbations of the quantum double Hamiltonians. (joint work with Matthew Cha and Pieter Naaijkens)
hide
MIT
Tue 20 Mar 2018, 4:00pm
Discrete Math Seminar
ESB 4127
Zarankiewicz's problem for semi-algebraic hypergraphs
ESB 4127
Tue 20 Mar 2018, 4:00pm-5:00pm

Abstract

Zarankiewicz’s problem asks for the largest possible number of edges in a graph with $n$ vertices that does not contain K_{s,t} for some fixed integers $s, t$. Recently, Fox, Pach, Sheffer, Sulk and Zahl considered this problem for semi-algebraic graphs, the ones whose vertices are points in Euclidean spaces and edges are defined by some semi-algebraic relations. They found an upper bound that only depends on the dimensions of those Euclidean spaces; this result is a vast generalization of the well-known Szemer\'edi-Trotter theorem and has many geometric applications. In this talk, we will explain this result and how to extend it to hypergraphs. Our proof uses a packing result in VC-dimension theory and the polynomial partitioning method. As an application, we find an upper bound for the number of unit d × d minors in a d × n matrix with no repeated columns.
hide
PhD Candidate: Alessandro Marinelli
Mathematics, UBC
Wed 21 Mar 2018, 12:30pm SPECIAL
Room 203, Graduate Student Centre, UBC
PhD Exam: The Unboundedness of the Maximal Directional Hilbert Transform
Room 203, Graduate Student Centre, UBC
Wed 21 Mar 2018, 12:30pm-2:30pm

Details

Abstract:
In this dissertation we study the maximal directional Hilbert transform operator associated with a set U of directions in the n-dimensional Euclidean space. This operator shall be denoted by H U. We discuss in detail the proof of the (p,p)-weak unboundedness of H U in all dimensions n ≥ 2 and all Lebesgue exponents 1 < p < +∞ if U contains infinitely many directions in IR^n.

This unboundedness result for H U is an immediate consequence of a lower estimate for the (p,p) norm of the operatorH U that we prove if the cardinality of U (denoted by #U) is finite. In this case, we prove that the aforementioned operator norm is bounded from below by the square root of log(#U) up to a positive constant depending only on p and n, for any exponent p in the range 1 < p < +∞ and any n ≥ 2.

These results were first proved by G. A. Karagulyan in the case n = p = 2. The structure of our argument follows Karagulyan’s, but includes the results that are necessary for the extension of the lower estimate to the case 1 < p < +∞ and to all dimensions n ≥ 2.

Finally, a review of the scientific literature on H U and related topics is also included.

Note for Attendees

Latecomers will not be admitted.
hide
PhD Candidate: Niki Myrto Mavraki
Mathematics, UBC
Wed 21 Mar 2018, 12:30pm SPECIAL
Room 200, Graduate Student Centre, UBC
PhD Exam: Unlikely intersections and Equidistribution with a Dynamical Perspective
Room 200, Graduate Student Centre, UBC
Wed 21 Mar 2018, 12:30pm-2:30pm

Details

Abstract:
In this thesis we investigate generalizations of a theorem by Masser and Zannier concerning torsion specializations of sections in a fibered product of two elliptic surfaces.

We consider the Weierstrass family of elliptic curves 𝐸𝐸𝑡𝑡∶𝑦𝑦2=𝑥𝑥3+𝑡𝑡 and points 𝑃𝑃𝑡𝑡(𝑎𝑎)=(𝑎𝑎,√𝑎𝑎3+𝑡𝑡)in 𝐸𝐸𝑡𝑡parametrized by non-zero 𝑡𝑡.

Given 𝛼𝛼,𝛽𝛽algebraic over 𝑄𝑄2 with rational ratio, we provide an explicit description for the set of parameters 𝑡𝑡=𝜆𝜆 such that 𝑃𝑃𝜆𝜆(𝛼𝛼) and 𝑃𝑃𝜆𝜆(𝛽𝛽) are simultaneously torsion for 𝐸𝐸𝜆𝜆. In particular, we prove that the aforementioned set is empty unless 𝛼𝛼/𝛽𝛽∈{−2,−1/2}. Furthermore, we show that this set is empty even when 𝛼𝛼/𝛽𝛽∉𝑄𝑄 provided that 𝛼𝛼 and 𝛽𝛽 have distinct 2-adic absolute values and the ramification index of 𝛼𝛼/𝛽𝛽 over 𝑄𝑄2is coprime with 6.

Our methods are dynamical. Using our techniques, we derive a recent result of Stoll concerning the Legendre family of elliptic curves 𝐸𝐸𝑡𝑡:𝑦𝑦2=𝑥𝑥(𝑥𝑥−1)(𝑥𝑥−𝑡𝑡), which itself strengthened earlier work of Masser and Zannier by establishing, as a special case, that there is no complex parameter 𝑡𝑡=𝜆𝜆∉{0,1} such that the points with x-coordinates 𝑎𝑎 and 𝑏𝑏 are both torsion in 𝐸𝐸𝜆𝜆, provided 𝑎𝑎,𝑏𝑏 have distinct reduction modulo 2.

We also consider an extension of Masser and Zannier's theorem in the spirit of Bogomolov's conjecture.

Let 𝐸𝐸→𝐵𝐵 be an elliptic surface defined over a number field 𝐾𝐾, where 𝐵𝐵 is a smooth projective curve, and let 𝑃𝑃:𝐵𝐵→𝐸𝐸 be a section defined over 𝐾𝐾 with non-zero canonical height. We use Silverman's results concerning the variation of the Neron-Tate height in elliptic surfaces, together with complex-dynamical arguments to show that the function 𝑡𝑡→ℎ𝐸𝐸𝑡𝑡(𝑃𝑃𝑡𝑡) satisfies the hypothesis of Thuillier and Yuan's equidistribution theorems. Thus, we obtain the equidistribution of points 𝑡𝑡∈𝐵𝐵 where 𝑃𝑃𝑡𝑡 is torsion. Finally, combined with Masser and Zannier's theorems, we prove the Bogomolov-type extension of their theorem. More precisely, we show that there is a positive lower bound on the height ℎ𝐴𝐴𝑡𝑡(𝑃𝑃𝑡𝑡), after excluding finitely many points 𝑡𝑡∈𝐵𝐵, for any `non- special' section 𝑃𝑃 of a family of abelian varieties 𝐴𝐴→𝐵𝐵 that split as a product of elliptic curves.

Note for Attendees

Latecomers will not be admitted.
hide
University of Washington
Wed 21 Mar 2018, 3:10pm
Probability Seminar
LSK 460
On Lambertian reflections and stirring coffee
LSK 460
Wed 21 Mar 2018, 3:10pm-4:10pm

Abstract


The Lambertian distribution, also known as Knudsen's Law, is a model for random reflections of light or gas particles from rough surfaces. I will present a mathematical "justification" of the Lambertian distribution. Then I will discuss a deterministic model inspired by stirring coffee. The analysis of the model will be partly deterministic, and partly based on the Lambertian distribution.


Joint work with O. Angel, M. Duarte, C.-E. Gauthier, J. San Martin, and S. Sheffield.


hide
University of Oregon
Wed 21 Mar 2018, 3:15pm
Topology and related seminars
ESB 4133
A structure theorem for RO(C_2)-graded cohomology
ESB 4133
Wed 21 Mar 2018, 3:15pm-4:15pm

Abstract

Computations in RO(G)-graded Bredon cohomology can be challenging and are not well understood, even for G=C_2, the cyclic group of order two.  In this talk I will present a structure theorem for RO(C_2)-graded cohomology with constant Z/2 coefficients that substantially simplifies computations.  The structure theorem says the cohomology of any finite C_2-CW complex decomposes as a direct sum of two basic pieces: shifted copies of the cohomology of a point and shifted copies of the cohomologies of spheres with the antipodal action.  I will give some examples and sketch the proof, which depends on a Toda bracket calculation.
hide
Colorado State
Wed 21 Mar 2018, 4:00pm SPECIAL
Algebraic Geometry Seminar / Number Theory Seminar
MATH 126
Algebraic intermediate Jacobians are arithmetic
MATH 126
Wed 21 Mar 2018, 4:00pm-5:00pm

Abstract

Consider a smooth projective variety over a number field.  The image of the associated (complex) Abel--Jacobi map inside the (transcendental) intermediate Jacobian is an abelian variety.  We show that this abelian variety admits a distinguished model over the number field.  Among other applications, this tool allows us to answer a recent question of Mazur; recover an old result of Deligne; and give new constructions of period maps over arithmetic bases.
hide
UBC Math
Fri 23 Mar 2018, 3:00pm
Department Colloquium
ESB 2012
Graduate Research Award: Clustering: a common thread between super-resolution image analysis and cancer
ESB 2012
Fri 23 Mar 2018, 3:00pm-4:00pm

Abstract

Clustering appears in many guises, playing important roles in diverse areas of cell biology. One such guise is the spatial clustering of proteins on the membrane of a cell. The ability of cell membrane proteins to cluster in response to stimuli is important to the normal function of many cells, but spontaneous, uncontrolled clustering can lead to cancer. Biologists are therefore keen to analyse protein clustering to better understand how cells function and gain insight into related diseases. This quest is assisted by super-resolution microscopy techniques that enable single molecules to be imaged down to nanoscale precision. In this talk, I will outline StormGraph, a graph-based clustering algorithm that I have developed for the analysis of protein clustering in super-resolution microscopy data. Using simulated data, I have found StormGraph to recover ground-truth clusters more accurately than current leading algorithms, and I have demonstrated its use on super-resolution microscopy data from normal and cancerous B-cells, our antibody-producing immune cells.

I will also provide a brief overview of how I intend to use clustering in multi-dimensional proteomic space to potentially improve personalized cancer therapies in the future. Tumours are heterogeneous populations of cells, and the activity of various signalling proteins can differ between cells within the same tumour. This intratumour heterogeneity is a key driver of resistance to cancer therapies, and should therefore be considered if trying to develop effective personalized therapies. I am working to develop suitable experiments and computational analysis to analyse this heterogeneity in B-cell tumours.

Note for Attendees

Refreshments will be served in ESB 4133 from 2:45 p.m.-3:00 p.m.
hide
UC Riverside
Mon 26 Mar 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126
Springer theory and hypertoric varieties
MATH 126
Mon 26 Mar 2018, 4:00pm-5:00pm

Abstract

The nilpotent cone has very special geometry which encodes interesting representation theoretic information.  It is expected that many of its special properties have analogues for general “symplectic singularities.”  This talk will discuss one such analogy for a class of symplectic singularities called hypertoric varieties.  The main result, joint with T. Braden, can be described as a duality between nearby and vanishing cycle sheaves on Gale dual hypertoric varieties.
hide
William Carlquist
Mathematics, UBC
Tue 27 Mar 2018, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
A numerical-solution-free multi-functional optimization method for parameter estimation in differential equations
ESB 4133 (PIMS Lounge)
Tue 27 Mar 2018, 12:30pm-1:30pm

Abstract

The process of optimally fitting a differential-equation model to data is usually approached in an iterative manner by solving the equations numerically with some choice of parameters and using some algorithm (e.g. gradient descent) to improve the choice of parameters with successive steps of the iteration. We propose a new method that steps back from an exact numerical method and instead allows the numerical solution to emerge as part of the optimization. We introduce the objective function (1-s) || x - data ||^2 + s || Dx - f(x;p) ||^2 where x is the model values, Dx=f(x;p) is the differential equation in discrete form (i.e. Dx is the discretization of the differential operator), where we must optimize for model values x and parameters p. We use s to implement niches in a genetic optimization algorithm and extract the best fit in the limit as s approaches 1. This method bypasses the need for implicit solution methods and, interestingly, admits conservative quantities, which allow us to gauge the accuracy of our optimization. I will discuss the theory, benefits, and examples of the method.
hide
Queen's University
Tue 27 Mar 2018, 2:00pm SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Ramification Theory for Arbitrary Valuation Rings in Positive Characteristic (talk 1)
ESB 4127
Tue 27 Mar 2018, 2:00pm-3:00pm

Abstract

In classical ramification theory, we consider extensions of complete discrete valuation rings with perfect residue fields. We would like to study arbitrary valuation rings with possibly imperfect residue fields and possibly non-discrete valuations of rank ≥ 1, since many interesting complications arise for such rings. In particular, defect may occur (i.e. we can have a non-trivial extension, such that there is no extension of the residue field or the value group).

We present some new results for Artin-Schreier extensions of arbitrary valuation fields in positive characteristic p. These results relate the “higher ramification ideal” of the extension with the ideal generated by the inverses of Artin-Schreier generators via the norm map. We also introduce a generalization and further refinement of Kato’s refined Swan conductor in this case. Similar results are true in mixed characteristic (0, p).

This is talk 1 of 2 by the speaker, and part of the PIMS Thematic Events on "Galois groups in arithmetic".
hide
Arizona State University
Tue 27 Mar 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
A uniqueness theorem for asymptotically cylindrical shrinking Ricci solitons
ESB 2012
Tue 27 Mar 2018, 3:30pm-4:30pm

Abstract

I will discuss some recent joint work with Lu Wang in which we prove that a shrinking gradient Ricci soliton which agrees to infinite order at spatial infinity with a generalized cylinder along some end must be isometric to the cylinder on that end. When the shrinker is complete, it must be globally isometric to the cylinder or else to a Z_2-quotient.  This work belongs to a larger program aimed at obtaining a structural classification of complete noncompact shrinking solitons.
hide
Colorado State University
Tue 27 Mar 2018, 4:00pm
Discrete Math Seminar
ESB 4127
An efficient Markov chain sampler for plane curves
ESB 4127
Tue 27 Mar 2018, 4:00pm-5:00pm

Abstract

 
hide
Queen's University
Wed 28 Mar 2018, 11:00am SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Ramification Theory for Arbitrary Valuation Rings in Positive Characteristic (talk 2)
ESB 4127
Wed 28 Mar 2018, 11:00am-12:00pm

Abstract

In classical ramification theory, we consider extensions of complete discrete valuation rings with perfect residue fields. We would like to study arbitrary valuation rings with possibly imperfect residue fields and possibly non-discrete valuations of rank ≥ 1, since many interesting complications arise for such rings. In particular, defect may occur (i.e. we can have a non-trivial extension, such that there is no extension of the residue field or the value group).

We present some new results for Artin-Schreier extensions of arbitrary valuation fields in positive characteristic p. These results relate the “higher ramification ideal” of the extension with the ideal generated by the inverses of Artin-Schreier generators via the norm map. We also introduce a generalization and further refinement of Kato’s refined Swan conductor in this case. Similar results are true in mixed characteristic (0, p).

This is talk 2 of 2 by the speaker, and part of the PIMS Thematic Events on "Galois groups in arithmetic".
hide
University of Washington
Wed 28 Mar 2018, 3:10pm
Probability Seminar
LSK 460
Geodesics in First-Passage Percolation
LSK 460
Wed 28 Mar 2018, 3:10pm-4:10pm

Abstract


First-passage percolation is a classical random growth model which comes from statistical physics. We will discuss recent results about the relationship between the limiting shape in first passage percolation and the structure of the infinite geodesics. This includes a solution to the midpoint problem of Benjamini, Kalai and Schramm. This is joint work with Daniel Ahlberg.


hide
Department of Biological Sciences, IISER Mohali, INDIA
Wed 28 Mar 2018, 3:15pm SPECIAL
Mathematical Biology Seminar
ESB 5104
Modelling Infectious Diseases: From Genomes to Populations (a PWIAS Public Talk)
ESB 5104
Wed 28 Mar 2018, 3:15pm-4:30pm

Abstract

 

Understanding incidence, spread, prevalence and control of an infectious disease requires a multidisciplinary approach that encompasses many fields of inquiry in Natural and Social Sciences. Several biological, environmental and economic/social/demographic factors govern the disease spread in a population. The overall pattern of a disease incidence is an outcome of the interaction of all these processes acting at different scales - from genetic epidemiology to public health - making it a complex multi-scale and interdisciplinary study.

Mathematical modelling of the disease process has been one of the oldest areas of study in Mathematical Biology. It has contributed significantly to the understanding of basic infection process, predicting future incidence to aid in taking immediate control measures, drug discovery, and health policy development. It uses application of concepts from different areas in mathematics, statistics and computational algorithms for data analysis and visualization. Each theoretical approach incorporates information from the biological, environmental, and social sciences, and offers understanding at different scales.

In this talk I will outline studies at three different scales to highlight the type of data required, variety of methods of analysis, and kinds of inferences/information that the analysis offers. I will show that comparative whole genome analysis of HIV-1, the pathogen responsible for AIDS, offers some insights into the differential evolution of HIV-1 genes; Understanding HIV-1 Reverse Transcriptase (RT) wild-type and mutant protein structures using graph theory allows us to uncover the drug resistance mechanisms in RT-drug mutants. Finally, at the population level modelling of disease spread, I will discuss our studies of Malaria using mathematical, statistical, and graphical approaches suitable for a diversity of fine and coarse-grained data from India.


Note for Attendees

 Refreshments are served in the PIMS lounge (ESB 4th floor) at 2:45PM 

Prof. Sinha is an International Visiting Research Scholar at the Peter Wall Institute for Advanced Studies (PWIAS); her hosts in the Department of Mathematics are Daniel Coombs and Leah Keshet. This public talk is shared between PWIAS, the UBC Mathematics Department, and the Pacific Institute for Mathematical Sciences, where she is also affiliated during her visit to UBC.

https://pwias.ubc.ca/event/modelling-infectious-diseases-genomes-populations
hide
XiaoLin Danny Shi
Harvard University
Wed 28 Mar 2018, 3:15pm
Topology and related seminars
ESB 4133
Real Orientations of Lubin-Tate Spectra
ESB 4133
Wed 28 Mar 2018, 3:15pm-4:15pm

Abstract

We show that Lubin--Tate spectra at the prime 2 are Real oriented and Real Landweber exact.  The proof is by application of the Goerss--Hopkins--Miller theorem to algebras with involution.  For each height n, we compute the entire homotopy fixed point spectral sequence for E_n with its C_2-action given by the formal inverse.  We study, as the height varies, the Hurewicz images of the stable homotopy groups of spheres in the homotopy of these C_2-fixed points.
hide
Columbia University
Wed 28 Mar 2018, 3:15pm SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Counting D_4-quartic fields ordered by conductor
ESB 4127
Wed 28 Mar 2018, 3:15pm-4:15pm

Abstract

We consider the family of D_4-quartic fields ordered by the Artin conductors of the corresponding 2-dimensional irreducible Galois representations. In this talk, I will describe ways to compute the number of such D_4 fields with bounded conductor. Traditionally, there have been two approaches to counting quartic fields, using arithmetic invariant theory in combination of geometry-of-number techniques, and applying Kummer theory together with L-function methods. Both of these strategies fall short in the case of D_4 fields since counting quartic fields containing a quadratic subfield of large discriminant is difficult. However, when ordering by conductor, these techniques can be utilized due to additional algebraic structure that the Galois closures of such quartic fields have, arising from the outer automorphism of D_4. This result is joint work with Ali Altug, Arul Shankar, and Kevin Wilson.
hide
University of Sherbrooke
Thu 29 Mar 2018, 3:15pm SPECIAL
Topology and related seminars
ESB 4133
Khovanov-type invariants for strong inversions
ESB 4133
Thu 29 Mar 2018, 3:15pm-4:15pm

Abstract

The symmetry group of a knot in the three-sphere is the mapping class group of the knot’s exterior. Elements of order two with fixed point set meeting the boundary of the knot exterior are called strong inversions, and a pair (K,h) is called a strongly invertible knot when h is a strong inversion in the symmetry group of K. Studying the equivalence of strongly invertible knots amounts to studying conjugacy classes of strong inversions. I will discuss how to construct invariants of strongly invertible knots using Khovanov homology. Some of this is joint work with Mike Snape and, time permitting, I will also discuss work in progress with Andrew Lobb.
hide
Jean-Marc Deshouillers
Bordeaux INP
Thu 29 Mar 2018, 3:30pm
Number Theory Seminar
MATH 126
Values of arithmetic functions at consecutive arguments
MATH 126
Thu 29 Mar 2018, 3:30pm-5:00pm

Abstract

We shall place in a general context the following result recently (*) obtained jointly with Yuri Bilu (Bordeaux), Sanoli Gun (Chennai) and Florian Luca (Johannesburg).

Theorem. Let τ(·) be the classical Ramanujan τ-function and let k be a positive integer such that τ(n) ≠ 0 for 1 ≤ n ≤ k/2. (This is known to be true for k < 1023 , and, conjecturally, for all k.) Further, let σ be a permutation of the set {1, ..., k}. We show that there exist infinitely many positive integers m such that |τ(m + σ(1))| < |τ(m + σ(2))| < ... < |τ(m + σ(k))|.

The proof uses sieve method, Sato-Tate conjecture, recurrence relations for the values of τ at prime power values.
(*) Hopefully to appear in 2018
hide
 
Top