Mathematics, UBC

Mon 1 Oct 2012, 3:00pm
Institute of Applied Mathematics
LSK 460

HotSpot Patterns of Urban Crime: Stability, Bifurcation, and Dynamics

LSK 460
Mon 1 Oct 2012, 3:00pm4:00pm
Abstract
The existence and stability of localized patterns of criminal activity
are studied for the reactiondiffusion model of urban crime that was
derived by Short et.~al.~[Math. Models. Meth. Appl. Sci., {\bf 18},
Suppl. (2008), pp.~12491267] as a continuum limit of an
agentbased model. Such patterns, characterized by the concentration
of criminal activity in localized spatial regions, are referred to as
hotspot patterns and they occur in a parameter regime far from the
Turing point associated with the bifurcation of spatially uniform
solutions. Singular perturbation techniques are used to construct
steadystate hotspot patterns in one and twodimensional spatial
domains. Explicit stability thresholds for these patterns are obtained
by first deriving and then analyzing a new class of nonlocal
eigenvalue problems. In a certain parameter regime of this model,
analytical and numerical methods are used to analyze the phenomena of
hotspot nucleation, whereby elevated regions of criminal activity
emerge ``spontaneously'' from a quiescent background. Finally, an
extended reactiondiffusion model that incorporates the effect of
police is analyzed, and optimal strategies to prevent the occurrence
of stable hotspots are discussed.
Joint work with: Theodore Kolokolnikov (Dalhousie), Simon Tse (UBC), and
Juncheng Wei (CUHK, UBC).
hide

UBC

Mon 1 Oct 2012, 3:00pm
Algebraic Geometry Seminar
ESB 2012

Toric embeddings over an arbitrary field

ESB 2012
Mon 1 Oct 2012, 3:00pm4:00pm
Abstract
The equivariant embeddings of a split torus have been wellknown since the 70s. The isomorphism classes of such embeddings are classified by combinatorial objects called fans (after Demazure). In this talk, we address the classification of the embeddings of a nonnecessary split torus and ask: Are the isomorphisms classes of such embeddings classified by Galoisstable fans? If time permits, we will discuss the analogous results in the setting of spherical homogeneous spaces.
hide

UBC

Mon 1 Oct 2012, 3:00pm
Harmonic Analysis Seminar
MATH 103 (pls note unusual location)

Euclidean Ramsey Theory

MATH 103 (pls note unusual location)
Mon 1 Oct 2012, 3:00pm4:00pm
Abstract
This talk concerns applications of ergodic theory to Euclidean Ramsey theory. We shall focus mainly on the problem of finding triangular configurations in thickened sets of positive density in the plane (due to Furestenberg, Katzenelson, and Weiss). The generalization for arbitrary configurations in dimension at least 2 (due to Ziegler) is also to be discussed.
hide

UBC

Tue 2 Oct 2012, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)

On the degeneracy of optimal transportation

ESB 2012 (in the new PIMS building)
Tue 2 Oct 2012, 3:30pm4:30pm
Abstract
It is well known that an upper and lower bound on the MongeAmp{\`e}re measure of a convex function u implies this function must actually be strictly convex. A lesser known result, also by Caffarelli, states that if the MongeAmp{\`e}re of u has only a lower bound, the contact set between u and a supporting affine function must have affine dimension strictly less than n/2. By means of a careful geometric construction involving the subdifferential, we give an alternative proof of Caffarelli's result, and extend the result to optimal transportation problems with cost functions satisfying the weak MaTrudingerWang condition. This talk is based on a joint work with YoungHeon Kim.
hide

UBC

Wed 3 Oct 2012, 3:00pm
Topology and related seminars
ESB 4127

Knotted geodesics on hyperbolic surfaces

ESB 4127
Wed 3 Oct 2012, 3:00pm4:00pm
Abstract
A closed geodesic on a surface can also be viewed as a closed orbit of the geodesic flow on the unit tangent bundle of the surface. In this talk I will discuss the main tool for studying the knotproperties of closed orbits of (three dimensional) flows. This tool is called a template, first defined and used by Birman and Williams to study the well known Lorenzbutterfly.
The theory of templates was first used for geodesic flows by Ghys. I will discuss questions related to his extraordinary result, that the closed geodesics on the modular surface equal the closed orbits on the Lorenz butterfly, and will discuss some generalization of his methods to other hyperbolic surfaces.
hide

UBC

Thu 4 Oct 2012, 11:00am
Algebraic Groups and Related Structures
Math 126

An introduction to Chow groups with examples and warning signs

Math 126
Thu 4 Oct 2012, 11:00am12:30pm
Abstract
Our goal will be to get a feeling for what Chow groups are and how do they "look like". We will discuss CH_0 of a smooth compact complex curve and see how the classical AbelJacobi theorem gives a very concrete description of it. We will then talk a little about the group of divisors on a smooth variety, for which the situation is not much worse. We will mention the group of zerodimensional cycles on a surface, which is sometimes considerably more complicated. Finally we will see that while the Chow groups can be defined for nonsmooth varieties, defining the intersection product is not a trivial matter at all.
hide

University of Maryland

Thu 4 Oct 2012, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126

Entropy conjugacy and other Borel relations, especially for countable state Markov shifts

Math 126
Thu 4 Oct 2012, 2:00pm3:00pm
Abstract
Suppose S: X > X and T: Y > Y are continuous selfmaps of metric spaces X,Y (especially, with X,Y compact). They are topologically conjugate if there is a homeomorphism h: X > Y such that hS = Th . Various equivalence relations coarser than topological conjuacy have been considered for such maps S,T including the following: entropy conjugacy (as defined by Bowen); entropy conjugacy (as defined by Buzzi); Borel conjugacy (h is only required to be a Borelbimeasurable bijection); Borel isomorphism after restriction to a set of measure one for every invariant Borel probability. I'll discuss theorems and questions around these ideas, especially with regard to countable state Markov shifts, for which another relation ("almost isomorphism", in the spirit of AdlerMarcus) is relevant. I'll include new results joint with Buzzi and Gomez, and also a new universality theorem of Mike Hochman.
hide

UBC

Thu 4 Oct 2012, 3:30pm
Number Theory Seminar
room ESB 2012 (PIMS)

Attracting cycles and critical orbits on Berkovich spaces

room ESB 2012 (PIMS)
Thu 4 Oct 2012, 3:30pm4:30pm
Abstract
Berkovich's rigid analytic spaces are pathconnected, Hausdorff, locally compact spaces that generalize nonarchimedean fields in a way that allows conducting analysis. We use them to prove nonarchimedean analogs of results in complex dynamics.
It is a classical result that over the complex numbers, whenever a rational function φ has a fixed point that is attracting but not superattracting, that is a fixed point z with 0 < φ'(z) < 1, there is a critical point of φ whose orbit is attracted to z. We show that a similar, but not identical, result holds over nonarchimedean fields, with applications to both global and local nonarchimedean dynamics.
hide

University of Maryland

Fri 5 Oct 2012, 3:00pm
Department Colloquium
Math Annex 1100

Shift equivalence and strong shift equivalence for positive matrices

Math Annex 1100
Fri 5 Oct 2012, 3:00pm4:00pm
Abstract
Shift equivalence and strong shift equivalence of matrices over a semiring are matrix relations of great significance for symbolic dynamics; they are also interesting simply for matrices. The classification of nonnegative integral matrices up to strong shift equivalence is equivalent to the classification of shifts of finite type, the basic systems of symbolic dynamics. This classification problem has been open for 40 years.
I'll discuss the meaning of these relations and recent results (joint with Kim and Roush) for the case of positive matrices with entries from a dense subring of the reals. These results are obtained by extending the path methods approach developed by Kim and Roush in the early 1990s, which is based on a study of paths of conjugate positive real matrices.
hide

UBC

Tue 9 Oct 2012, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)

Forward Discrete SelfSimilar Solutions of the NavierStokes Equations

ESB 2012 (in the new PIMS building)
Tue 9 Oct 2012, 3:30pm4:30pm
Abstract
Extending the work of Jia and Sverak on selfsimilar solutions of the NavierStokes equations, we show the existence of large, forward, discrete selfsimilar solutions.
hide

UBC

Wed 10 Oct 2012, 3:00pm
Probability Seminar
ESB 2012

Extinction time of the contact process on finite trees

ESB 2012
Wed 10 Oct 2012, 3:00pm4:00pm
Abstract
We consider the contact process on finite trees. We assume that
the infection rate is larger than the critical rate for the onedimensional
process. We show that, for any sequence of trees with increasing number of
vertices and degree bounded by a universal constant, the expected
extinction time of the process grows exponentially. Additionally, the
extinction time divided by its expectation converges in distribution to the
unitary exponential distribution. This is joint work with Thomas Mountford,
JeanChristophe Mourrat and Qiang Yao.
hide

UBC

Wed 10 Oct 2012, 3:00pm
Topology and related seminars
ESB 4127

Topology meets essential dimension

ESB 4127
Wed 10 Oct 2012, 3:00pm4:00pm
Abstract
The talk will be an extended advertisement of a program to apply topological ideas to computation of essential dimension of groups.
The essential dimension of a group G measures to what extent every generically free action of G on an algebraic variety can be "compressed". For the symmetric group S_n, the essential dimension is directly related to the classical question how much an algebraic equation of degree n can be simplified by a rational change of variables.
I will introduce a topological approach to obtaining lower bounds on essential dimension. I will then survey some (nontopological) advances in theory of essential dimension and discuss some parallels in topology. Finally I will speculate on the possibility to relate results in the theory of topological group actions and results on essential dimension in a way that might benefit both fields.
hide

UBC

Thu 11 Oct 2012, 11:00am
Algebraic Groups and Related Structures
Math 126

An introduction to Chow groups II

Math 126
Thu 11 Oct 2012, 11:00am12:30pm
Abstract
We will continue the discussion from the previous talk on the basic ideas of Chow theory. We review the basic properties that make the Chow functor to be an oriented BorelMoore homology theory, and then we will discuss some further topics including their equivariant version, their operational version and their universal version.
hide

SFU

Thu 11 Oct 2012, 3:30pm
Number Theory Seminar
room ESB 2012 (PIMS)

On a problem about Mahler functions

room ESB 2012 (PIMS)
Thu 11 Oct 2012, 3:30pm4:30pm
Abstract
Let K be a field of characteristic zero and let k and l be two multiplicatively independent positive integers. We prove the following result: a power series F(x) in K[[x]] satisfies both a k and a lMahler type functional equation if and only if it is a rational function. This proves a conjecture of Loxton and van der Poorten. This is joint work with Boris Adamczewski.
hide

Texas A&M University

Mon 15 Oct 2012, 3:00pm
Algebraic Geometry Seminar
ESB 2012

Singular loci of cominuscule Schubert varieties

ESB 2012
Mon 15 Oct 2012, 3:00pm4:00pm
Abstract
The Schubert subvarieties of a rational homogeneous variety X are distinguished by the fact that their homology classes form an additive basis of the integer homology of X. In general, the Schubert varieties are singular.
The cominuscule rational homogeneous varieties are those admitting the structure of a compact Hermitian symmetric space (eg. complex Grassmannians). In this case, typedependent characterizations of the singular loci are known.
I will discuss a typeindependent description, by representation theoretic data, of the singular loci. The result is based on a characterization (joint with D. The) of the Schubert varieties by an nonnegative integer and a marked Dynkin diagram.
(If there is time left, I will discuss the project in which the integerdiagram characterization arose as a technical lemma. This work aims to determine whether or not the Schubert classes admit any algebraic representatives (other than the Schubert varieties). It is a remarkable consequence of Kostant's work that these algebraic representatives are solutions of a system of PDE; as a consequence, differential geometric techniques may be applied to this algebrotopological question.)
hide

Schlumberger DBR Technology Center

Mon 15 Oct 2012, 3:00pm
Institute of Applied Mathematics
LSK 460

A Model of Asphaltene Deposition in Production Pipelines

LSK 460
Mon 15 Oct 2012, 3:00pm4:00pm
Abstract
Asphaltene deposition is one of the important problems of
oil production that requires an accurate predictive modeling.
Uncontrolled deposition of asphaltenes may lead to a significant
reduction of oil production, or even to a total pipe plugging. We
developed an asphaltene deposition model in a pipeline. The model is
based on data, which are obtained by experiments performed in a
Couette device, where the inner cylinder rotates, and deposition on
the outer wall is studied. A detailed theoretical analysis of an
applicability of a Couette device for imitation of the asphaltene
deposition in a pipe flow is presented. A hypothesis stating that the
asphaltene deposition is a particle size controlled process is
accepted. A population balance model is employed for modeling the
particle size evolution. A concept of the critical particle size is
introduced; only particles that are smaller than the critical size
can deposit. The model developed contains only three parameters that
are determined experimentally by using a Couette device. The model of
asphaltene deposition in a Couette device allows accurate describing
the deposit mass growth in time. Performance of the deposition model
for a pipeline with the coefficients obtained by a laboratory Couette
device is also demonstrated.
hide


Mon 15 Oct 2012, 3:00pm
Harmonic Analysis Seminar
Math 126

Corners in dense subsets of P^d

Math 126
Mon 15 Oct 2012, 3:00pm4:00pm
Abstract
FurstenbergKatznelson's Theorem states that if "A" is a subset of Z^d with
positive upper density then for any finite set F of Z^d, A contains an affine image of F. We
wish to prove analogue theorem in prime tuples P^d where positive upper density is replaced by
relative upper density in P^d. This is partially done by Magyar and Cook in the case that no
two points in F have a common projection on some axis. When we count such configurations P^d
behaves like a random subset of Z^d with density(1/log N)^d but this is not true in general
since P^d has direct product structure. In this talk, we will discuss how to use hypergraph
approach and Gowers' Transference Principle to deal with the case that F is a corner (i,e,.
simplex of the form {(x_1,..,x_d),(x_1+s,x_2,..,x_d),...,(x_1,...,x_d+s)},s \neq 0). We expect
that the same method should also work for any finite set F. This is a joint work with Akos
Magyar.
hide

Texas A&M

Tue 16 Oct 2012, 3:00pm
Algebraic Groups and Related Structures
Math 126

Schubert varieties as variations of Hodge structure.

Math 126
Tue 16 Oct 2012, 3:00pm4:00pm
Abstract
I will describe recent work that characterizes the Schubert varieties that arise as variations of Hodge structure (VHS). I will also discuss the central role that these Schubert VHS play in our study of general VHS. In particular: (i) infinitesimally their orbits under the isotropy action `span' the space of all VHS, yielding a complete description of the infinitesimal VHS; (ii) the cohomology classes dual to the Schubert VHS form an (integral) basis of the invariant characteristic cohomology associated to the system of PDE characterizing VHS.
hide

UBC

Tue 16 Oct 2012, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building) TBA

Absolutely continuous spectrum for random Schrödinger operators on treestrips of finite conetype.

ESB 2012 (in the new PIMS building) TBA
Tue 16 Oct 2012, 3:30pm4:30pm
Abstract
One of the biggest challenges in the field of random Schrödinger operators is to prove the existence of absolutely continuous spectrum for the Anderson model for small disorder in dimensions greater equal to 3. So far, the existence of absolutely continuous spectrum is only known for models on infinitedimensional tree structures. The first proof, done by Abel Klein for a regular tree, dates back to 1994.
Recent developments considered trees of finite cone type and cross products of trees with finite graphs, so called treestrips. I will present a proof for the existence of absolutely continuous spectrum for models on treestrips of finite cone type. The proof uses a version of the Implicit Function Theorem in Banach spaces which are constructed by a supersymmetric formalism using Grassmann variables.
hide

UBC

Tue 16 Oct 2012, 4:00pm
Discrete Math Seminar
Math 126

On the structure of lines containing many points of a cartesian product

Math 126
Tue 16 Oct 2012, 4:00pm5:00pm
Abstract
In 1997 Elekes showed the following. Suppose you have an $n\times n$ cartesian product $A \times B$ in the real plane. If $cn$ lines each contain at least $cn$ points of the cartesian product then $c'n$ of the lines are parallel or $c'n$ of them have the same intersection point. We show that this result can be extended by considering fewer lines. Specifically, if we have $cn^{2/3+\beta/3}$ lines each containing $c'n$ points of the cartesian product then $c''n^{\beta} of the lines are parallel or have the same intersection point. We used this to extend a theorem of Elekes and Ronyai regarding the structure of a surface containing many points of a cartesian product. These results give a proof of a conjecture of Purdy saying that if two collinear sets in the plane give too few distinct distances then the lines are parallel or orthogonal. This is joint work with Jozsef Solymosi and Frank de Zeeuw.
hide


Tue 16 Oct 2012, 4:00pm
SPECIAL
One Time Event
LSK 200

Graduate Student Forum

LSK 200
Tue 16 Oct 2012, 4:00pm5:30pm
Details
hide

UBC

Wed 17 Oct 2012, 3:00pm
Topology and related seminars
ESB 4133 (PIMS Lounge)

Homotopy colimits of classifying spaces of finite groups and Ktheory

ESB 4133 (PIMS Lounge)
Wed 17 Oct 2012, 3:00pm4:00pm
Abstract
Let G be a finite group, we consider the homotopy colimit of classifying spaces of abelian subgroups of G. This space is a K(\pi,1) for certain finite groups, but there are examples when the space has nonvanishing higher homotopy groups. I will also talk about the complex Ktheory of this space and give some examples.
hide

UBC

Wed 17 Oct 2012, 3:00pm
Probability Seminar
ESB 4127

Half planar triangulations

ESB 4127
Wed 17 Oct 2012, 3:00pm4:00pm
Abstract
Planar maps are embeddings of graphs on compact orientable
surfaces. We shall consider a special class of maps: triangulations with an
infinite simple boundary. We shall consider measures supported on this
space satisfying two natural properties: translation invariance and domain
Markov property. We shall show these two characters completely characterize
them. The methods reveal some standard maps and some mysterious maps of
hyperbolic nature.
hide

UBC

Thu 18 Oct 2012, 11:00am
Algebraic Groups and Related Structures
Math 126

On canonical dimension in the world of chow groups

Math 126
Thu 18 Oct 2012, 11:00am12:30pm
Abstract
We will define the canonical dimension of a smooth projective variety and compute it in the case of quadratic surfaces.
hide

University of Arizona

Thu 18 Oct 2012, 3:30pm
Number Theory Seminar
room ESB 2012 (PIMS)

A conjecture relating cup products of cyclotomic units and modular symbols

room ESB 2012 (PIMS)
Thu 18 Oct 2012, 3:30pm4:30pm
Abstract
I will discuss a conjecture which provides a relationship between Manin symbols in the homology of modular curves and cup products of cyclotomic units in Galois cohomology with restricted ramification. I hope to be able to give something of an idea of its meaning, with an eye towards generalization. I will also relate recent progress by Fukaya and Kato that essentially proves the conjecture under a mild but difficult to remove hypothesis.
hide

UBC

Mon 22 Oct 2012, 3:00pm
Algebraic Geometry Seminar
ESB 2012

Eigenvalues of hermitian matrices and equivariant cohomology of Grassmannians

ESB 2012
Mon 22 Oct 2012, 3:00pm4:00pm
Abstract
One remarkable application of classical Schubert calculus on the cohomology of the Grassmannian is its close connection to the eigenvalue problem on sums of hermitian matrices. The eigenvalue problem asks: Given three sequences of real numbers, do there exist hermitian matrices A+B=C with eigenvalues given by the three sequences? This problem has a generalization to eigenvalues of majorized sums of hermitian matrices where we replace "A+B=C" with "A+B>C".
In this talk, I discuss joint work with D. Anderson and A. Yong where we show that the eigenvalue problem on majorized sums is related to the Schubert calculus on the torusequivariant cohomology of the Grassmannian in the same way that classical Schubert calculus is related to eigenvalue problem on usual sums of Hermitian matrices. One consequence of this connection is a generalization of the celebrated saturation theorem to Tequivariant Schubert calculus.
hide

CNRS and Université Joseph Fourier

Tue 23 Oct 2012, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)

Nondifferentiability locus of distance functions and Federer's curvature measures

ESB 2012 (in the new PIMS building)
Tue 23 Oct 2012, 3:30pm4:30pm
Abstract
I will present an upper bound on the (d1)volume and covering numbers of a filtration of the nondifferentiability locus of the distance function of a compact set in R^d. A consequence of this upper bound is that the projection function to a compact subset K depends in a Hoelder way on the compact set, in the L^1 sense. This in turn implies that Federer's curvature measure of a compact set with positive reach can be reliably estimated from a Hausdorff approximation of this set, regardless of any regularity assumption on the approximation.
hide

Muenster

Tue 23 Oct 2012, 4:00pm
SPECIAL
PIMS Seminars and PDF Colloquiums
ESB 4127

IwahoriHecke algebras are Gorenstein Part II (Lecture)

ESB 4127
Tue 23 Oct 2012, 4:00pm5:00pm
Abstract
In the local Langlands program the (smooth) representation theory of padic reductive groups G in characteristic zero plays a key role. For any compact open subgroup K of G there is a so called Hecke algebra H(G,K). The representation theory of G is equivalent to the module theories over all these algebras H(G,K). Very important examples of such subgroups K are the Iwahori subgroup and the prop Iwahori subgroup. By a theorem of Bernstein the Hecke
algebras of these subgroups (and many others) have finite global dimension.
In recent years the same representation theory of G but over an algebraically closed field of characteristic p has become more and more important. But little is known yet. Again one can define analogous Hecke algebras. Their relation to the representation theory of G is still very
mysterious. Moreover they are no longer of finite global dimension. In joint work with R. Ollivier we prove that over any field the algebra H(G,K), for K the (prop) Iwahori subgroup, is Gorenstein.
hide

South Australia

Wed 24 Oct 2012, 3:00pm
Probability Seminar
ESB 2012

Why does clustered network connectivity give rise to bistable neuronal dynamics in simulations of large networks of cortical neurons, driven by Poisson spike trains?

ESB 2012
Wed 24 Oct 2012, 3:00pm4:00pm
Abstract
Although directed random graph models are frequently used in modeling the electrical activity of networks of cortical neurons, experimental results consistently reveal that the actual network topology is complex, and tends to be clustered locally. This suggests that the random network assumption is unrealistic and that when analysing population dynamics in cortical networks, it is necessary to employ directed network models that incorporate clustering.
In this seminar I shall describe simulation results that demonstrate that replacing random connectivity with clustered connectivity can induce instability in subsets of neurons, in terms of significantly increased firing rates. Moreover, it is shown that one specific network topology gives rise to slow bistable switching between low and high states.
The aim of presenting this seminar is not to describe finished mathematical work, but rather to seek collaboration or assistance with finding mathematical explanations that predict that clustered connectivity can lead to the bistable or unstable states observed in simulations.
hide

UBC

Wed 24 Oct 2012, 3:00pm
Undergraduate Colloquium
MATH 104

Coding Theory and Practice

MATH 104
Wed 24 Oct 2012, 3:00pm4:00pm
Abstract
UBC/UMC is the Undergraduate Mathematics Colloquium at UBC.
These talks are for undergraduates interested in mathematics and mathematical research. They are put on by professors, senior graduate students and visitors to the department. Graduate students are also invited to attend.
Title: Coding Theory and Practice
Abstract: In this talk, we will introduce the framework of coding theory, including some classical results, open problems and applications to data transmission and storage.
hide


Thu 25 Oct 2012, 9:00am
SPECIAL
One Time Event
Graduate Student Center, Room 200

Doctoral Exam

Graduate Student Center, Room 200
Thu 25 Oct 2012, 9:00am11:30am
Details
In this thesis we present a reduction theory for the symmetrizable split maximal KacMoody groups. However there are many technical difficulties before one can even formulate a reduction theorem. Combining the two main approaches commonly seen in the literature we define a group, first over any field of characteristic zero and then on any commutative ring of characteristic zero. Then we prove a number of structural properties of the group such as representation in the highest weight modules, existence of a Tits system and an Iwasawa decomposition over $\RR$ and $\CC$. Finally we arrive at reduction theory which can only hold for part of the group.
hide

UBC

Thu 25 Oct 2012, 11:00am
Algebraic Groups and Related Structures
Math 126

Further definitions of Canonical Dimension

Math 126
Thu 25 Oct 2012, 11:00am12:00pm
Abstract
We cover some further definitions of canonical dimensions for smooth projective varieties.
hide

UBC

Thu 25 Oct 2012, 3:30pm
Number Theory Seminar
room ESB 2012 (PIMS)

Generalized Mordell curves, generalized Fermat curves, and the Hasse principle

room ESB 2012 (PIMS)
Thu 25 Oct 2012, 3:30pm4:30pm
Abstract
We show that for each prime p congruent to 1 (mod 8), there exists a threefold X_{p} such that the existence of certain rational points on X_{p} produces families of generalized Mordell curves and of generalized Fermat curves that are counterexamples to the Hasse principle explained by the Brauer–Manin obstruction. We also introduce a notion of the descending chain condition (DCC) for sequences of curves, and prove that there are sequences of generalized Mordell curves and of generalized Fermat curves satisfying DCC.
hide

University of Chicago

Fri 26 Oct 2012, 3:00pm
SPECIAL
Department Colloquium
MATX 1100

PIMS/UBC Distinguished Colloquium: Differentiability of Lipschitz functions and tangents of sets

MATX 1100
Fri 26 Oct 2012, 3:00pm4:00pm
Abstract
Abstract: We will show how elementary product decompositions of measures can detect directionality in sets, and show how this can be used to describe nondifferentiability sets of Lipschitz functions on R^n, and to understand the phenomena that occur because of behaviour of Lipschitz functions around the points of null sets.
In order to prove this we will need to prove results about the geometry of sets of small Lebesgue measure: we show that sets of small measure are always contained in a "small" collection of Lipschitz surfaces.
The talk is based on a joint work with G. Alberti, P. Jones and D. Preiss.
hide

Northwestern University

Mon 29 Oct 2012, 3:00pm
Algebraic Geometry Seminar
ESB 2012

Strictifying Higher Principal Bundles

ESB 2012
Mon 29 Oct 2012, 3:00pm4:00pm
Abstract
Higher stacks arise in many contexts in algebraic geometry and differential topology. The simplest type are higher principal bundles, special cases of which include principal bundles and ngerbes. Locally, these objects are presentable by higher cocycles on a hypercover. With ordinary principal bundles, we obtain a bundle from a cocycle by using the cocycle to construct a Lie groupoid over the trivial bundle on the cover, and then passing to its orbit space. We establish the existence of an analogous construction for arbitrary higher principal bundles. Unpacking this construction in examples, we recover the familiar definitions of principal bundles, bundle gerbes, multiplicative gerbes and their equivariant versions, now seen as instances of a single construction. Applications beyond this include establishing a representability criterion for connected simplicial presheaves, and a Lie's 3rd theorem for finite dimensional L_ooalgebras.
hide

University of Chicago

Mon 29 Oct 2012, 3:00pm
Harmonic Analysis Seminar
Math 126

TBA

Math 126
Mon 29 Oct 2012, 3:00pm4:00pm
Abstract
hide

The University of British Columbia

Tue 30 Oct 2012, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133

Reweighted algorithms for sparse signal recovery

ESB 4133
Tue 30 Oct 2012, 12:30pm1:30pm
Abstract
Sparse signal recovery has been dominated by the basis pursuit denoise (BPDN) problem formulation for over a decade. In this paper, we propose an algorithm that outperforms BPDN in finding sparse solutions to underdetermined linear systems of equations at no additional computational cost. Our algorithm, called WSPGL1, is a modification of the spectral projected gradient for minimization (SPGL1) algorithm in which the sequence of LASSO subproblems are replaced by a sequence of weighted LASSO subproblems with constant weights applied to a support estimate. The support estimate is derived from the data and is updated at every iteration. The algorithm also modifies the Pareto curve at every iteration to reflect the new weighted minimization problem that is being solved. We demonstrate through extensive simulations that the sparse recovery performance of our algorithm is superior to that of minimization and approaches the recovery performance of iterative reweighted (IRWL1) minimization of Candès, Wakin, and Boyd, although it does not match it in general. Moreover, our algorithm has the computational cost of a single BPDN problem.
hide

UBC

Tue 30 Oct 2012, 4:00pm
Discrete Math Seminar
Math 126

On the integer distances problem

Math 126
Tue 30 Oct 2012, 4:00pm5:00pm
Abstract
In this talk we will discuss the integer distances problem: can we find n points in a general position on the plane such that all the distances between the points are integers? So far this question has been resolved up to 7 points. We will present results related to the problem and our recent efforts to find 8 points with integer distances.
hide

University of Southern California

Wed 31 Oct 2012, 3:00pm
Topology and related seminars
ESB 4127

The Brauer Group and Obstruction Theory

ESB 4127
Wed 31 Oct 2012, 3:00pm4:00pm
Abstract
The study of central simple algebras over a field is a venerable topic in ring theory. There is a generalization of central simple algebras to schemes in the étale topology (in fact to arbitrary ringed sites) due to Grothendieck. The group of equivalence classes of Azumaya algebras over X is known as the Brauer group of X. By comparing the étale topology on a smooth complex variety X with the classical topology, we are able to use results from classical obstruction theory in order to obstruct the existence of certain Azumaya algebras. After giving an introduction to Azumaya algebras and the Brauer group, we shall present one such result, which furnishes lower bounds on the ranks of Azumaya algebras on spaces of low cohomological dimension.
hide

Note for Attendees
Refreshments will be served at 2:45 p.m. in MATH 125 before the colloquium.