Mathematics Dept.
  Events
McGill
Tue 24 Oct 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
An isometric embedding problem and related geometric inequalities
ESB 2012
Tue 24 Oct 2017, 3:30pm-4:30pm

Abstract

Solutions to the classical Weyl problem by Nirenberg and Pogorelov
play fundamental role in the notion of quasi local masses and positive quasi
local mass theorems in general relativity. An interesting question in
differential geometry is whether one can isometrically embed compact surfaces
with positive Gauss curvature to a general 3 dimensional ambient space. Of
particular importance is the anti de Sitter Schwarzchild space in general
relativity.  We discuss some recent progress in this direction, the a priori
estimates for embedded surfaces in a joint work with Lu, the openness and
non-rigidity results of Li -Wang, and a new quasi local type inequality of
Lu-Miao. We will also discuss open problem related to isometric embeddings to
ambient spaces with horizons.
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UBC
Tue 24 Oct 2017, 4:00pm
Discrete Math Seminar
ESB 4127
Disjoint Cycles and Equitable Colorings in Graphs
ESB 4127
Tue 24 Oct 2017, 4:00pm-5:00pm

Abstract

The Corradi-Hajnal Theorem gives a minimum-degree condition for the existence of a given number of vertex-disjoint cycles in a simple graph. We discuss a number of variations on the Corradi-Hajnal Theorem, changing both the nature of the necessary condition (for example, minimum degree sum instead of minimum degree) and the kind of subgraph whose existence is desired. We also briefly discuss the connections between these types of theorems and equitable graph colourings.

 

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Krishanu Sankar
UBC
Wed 25 Oct 2017, 3:15pm
Topology and related seminars
ESB 4133
Symmetric Powers and the Dual Steenrod Algebra - Part 1
ESB 4133
Wed 25 Oct 2017, 3:15pm-4:15am

Abstract

The mod $p$ Steenrod algebra is the (Hopf) algebra of

stable operations on mod $p$ cohomology, and in part

measures the subtle behavior of $p$-local homotopy theory

(as opposed rational homotopy theory, which is much simpler).

A classical theorem of Dold-Thom tells us that the infinite

symmetric power of the $n$-dimensional sphere is the Eilenberg-Maclane

space K(Z, n),and one can use an appropriate modification of this

construction to compute the dual Steenrod algebra. The infinite

symmetric power of the sphere spectrum has a filtration whose

$k$-th cofiber miraculously turns out to be the Steinberg summand

(from modular representation theory of GL_k(F_p)) of the

classifying space of (Z/p)^k. This opens the door for slick

computations - for example, the Milnor indecomposables can

be picked out as explicit cells.

 

In this talk, I will introduce the concepts and results

chronologically. I will also include hands-on homotopy

theory computations as time permits.

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Alain Prat
UBC Math
Thu 26 Oct 2017, 12:30pm
Lunch Series on Teaching & Learning
Math 126
Working against the WeBWork clock: What are the behaviour patterns of students who struggle to complete online calculus assignments?
Math 126
Thu 26 Oct 2017, 12:30pm-1:30pm

Abstract

Since 2010, the math department at UBC has been gradually adopting the WeBWork online homework system in most first and second year courses. Instructors typically give students several days to complete their WeBWork assignments, and allow students several attempts at each problem. Despite this, many students struggle to complete their online assignments. In this talk, I'll discuss how the timing of answer submissions recorded in WeBWork log files can reveal the behaviour patterns of students who struggle with WeBWork. In particular, students who don't complete the WeBWork start the assignments closer to the deadline, have shorter login sessions and don't persist for as long once they encounter a problem they can't solve. I'll discuss what these observations reveal about the mindset of struggling students, and how assignments could be restructured to help increase their completion rate.
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Nikhil Kher
Fri 27 Oct 2017, 12:00pm
Graduate Student Seminar
MATH 203
Operator Semigroups and Hille Yosida Theorem
MATH 203
Fri 27 Oct 2017, 12:00pm-1:00pm

Abstract

Semigroups are useful in solving a large class of problems known as evolution equations. These kind of equations often appear in many disciplines including physics, chemistry, biology and engineering. I will be discussing an introduction to theory of C0-semigroups on Banach spaces. We then discuss uniformly continuous semigroups and prove some important results and characterizations related to them. Following which, we present examples of how new semigroups can be constructed out of a given semigroup. We associate a generator to a C0-semigroup and illustrate their properties by means of some theorems. Subsequently we prove Hille-Yosida theorem, which provides a necessary and sufficient condition for an unbounded operator on a Banach space to be a generator of a contraction C0-semigroup. This was proved in 1948 by mathematicians E. Hille and K. Yosida. We also prove Feller-Miyadera-Phillips theorem which generalizes Hille-Yosida theorem. This was proved around 1952. If time permits I'll do some other interesting stuff related to theory of C_0-semigroups.
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Jim Bryan
UBC
Mon 30 Oct 2017, 4:00pm
Algebraic Geometry Seminar
MATH 126
Donaldson-Thomas invariants of the banana manifold and elliptic genera.
MATH 126
Mon 30 Oct 2017, 4:00pm-5:00pm

Abstract

The Banana manifold (or bananafold for short), is a compact Calabi-Yau threefold X which fibers over P^1 with Abelian surface fibers. It has 12 singular fibers which are non-normal toric surfaces whose torus invariant curves are a banana configuration: three P^1’s joined at two points, each of which locally look like the coordinate axes in C^3. We show that the Donaldson-Thomas partition function of X (for curve classes in the fibers) has an explicit product formula which, after a change of variables is the same as the generating function for the equivariant elliptic genera of Hilb(C^2), the Hilbert scheme of points in the plane.
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