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Tuesday, April 25, 2017 — 3:30 PM EDT

Michael Deveau, Department of Pure Mathematics, University of Waterloo

"The Slaman-Wehner Family"

We introduce the Slaman-Wehner family, and use it to build a structure with an important property: it has no computable copy, but is computable in any non-computable set. In other words, this structure's degree spectrum is equal to the set of non-computable sets.

MC 5403

Tuesday, April 25, 2017 — 2:30 PM EDT

Shubham Dwivedi, Department of Pure Mathematics, University of Waterloo

"Simons' Inequality and consequences"

We will prove the Simons' Inequality which is satisfied by the laplacian of the normed square of the second fundamental form of any minimal hypersurface in $\mathbb{R}^n$. We will then prove various consequences of the inequality, including results of Choi and Schoen, Hopf and that of Schoen/Leon Simon/Yau.

MC 5479

Thursday, April 20, 2017 — 2:30 PM EDT

Akos Nagy, Department of Pure Mathematics, University of Waterloo

"A compactness theorem for the Seiberg–Witten equation with multiple spinors in dimension three --- Part III"

I will continue with Section 4 of the Walpuski-Haydys paper: I will introduce the frequency function, state a couple important properties of it, and give outline of how it is used in the proof of the Main Theorem. If time permits, I will talk about the proofs of the properties.

MC 5479

Wednesday, April 19, 2017 — 3:30 PM EDT

Be'eri Greenfeld, Bar Ilan University

"Around and beyond the Koethe problem"

Tuesday, April 18, 2017 — 3:30 PM EDT

Jonny Stephenson, Department of Pure Mathematics, University of Waterloo

"Sets which are not the spectrum of any structure"

We continue our analysis of spectra, and show that no spectrum can be the Turing-upward closure of an F_sigma family of reals, unless that  upward closure is already an enumeration upper cone. We will see that, as in the case of the "no two cones" theorem, the key to the proof is to construct a suitably generic copy of a structure to see that it cannot possibly have the indicated spectrum.

MC 5403

Tuesday, April 18, 2017 — 2:30 PM EDT

Anthony McCormick, Department of Pure Mathematics, University of Waterloo

"Introduction to the Spencer Complex"

We'll begin discussing the idea behind the Spencer complex associated to a linear partial differential operator between vector bundles. To do this, we'll introduce jet bundles, prolongations and the definition of the principal symbol using this machinery.

MC 5479

Thursday, April 13, 2017 — 2:30 PM EDT

Shubham Dwivedi, Department of Pure Mathematics, University of Waterloo

"Simons' Inequality and consequences"

We will prove the Simons' Inequality which is satisfied by the laplacian of the normed square of the second fundamental form of any minimal hypersurface in $\mathbb{R}^n$. We will then prove various consequences of the inequality, including results of Choi and Schoen, Hopf and that of Schoen/Leon Simon/Yau.

MC 5479

Thursday, April 13, 2017 — 12:30 PM EDT

Diana Castaneda Santos, Department of Pure Mathematics, University of Waterloo

"The end of the Quasiseparated talk and the beginning of a new age"

We will finish our discussion on topological properties of schemes.  We will finally define quasiseparated schemes and see how they are related with quasicompact schemes. Additionally, we will start section 5.3. talking about the communication lemma, which is a convenient way to study properties on schemes by looking at properties on any affine open covering.

MC 5479

Tuesday, April 11, 2017 — 3:30 PM EDT

Jonny Stephenson, Department of Pure Mathematics, University of Waterloo

"Degree Spectra"

Last week we saw that every countable ideal in the enumeration degrees is the co-spectrum of some structure. Now we will consider what sets of degrees are spectra of structures. We will see that the situation is quite different, and that there are a number of classes which cannot be the spectrum of any structure. In particular, no nontrivial countable union of enumeration upper cones can be the spectrum of any structure.

MC 5403

Tuesday, April 11, 2017 — 2:30 PM EDT

Panagiotis Gianniotis, Department of Pure Mathematics, University of Waterloo

"A heat flow for special metrics II"

This is the second talk on the paper of Weiss and Witt 'A heat flow on special metrics'. In this talk, we will implement DeTurck's trick to the Dirichlet flow and show that the resulting equation is parabolic. Then we will focus on the issue of stability around the set of critical points for the Dirichlet functional.

MC 5479

Friday, April 7, 2017 — 2:30 PM EDT

Teng Fei, Columbia University

"A construction of infinitely many solutions to the Strominger system"

Wednesday, April 5, 2017 — 2:30 PM EDT

Manousos Maridakis, Rutgers University

"Lojasiewicz-Simon gradient inequalities with applications to Yang-Mills pairs and Harmonic maps"

Tuesday, April 4, 2017 — 3:00 PM EDT

Jonny Stephenson, Department of Pure Mathematics, University of Waterloo

"Co-spectra"

The co-spectrum of a structure is the family of sets coded by the structure. This is a measure of how well we can encode information in the structure. We will see that every countable ideal in the e-degrees is the co-spectrum of a structure, and give a generalization of Richter's result on c.e.-minimal pairs.

MC 5403

Monday, April 3, 2017 — 11:30 AM EDT

Brett Nasserden, Department of Pure Mathematics, University of Waterloo

"Matroidal flips and related ideas/constructions"

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