The UTGSU Conference Bursary was created in 2016 to financially assist UTGSU Members attending and/or presenting at academic conferences. The amount of a single bursary is $250, regardless of conference location or estimated expenses. A total of 120 bursaries are distributed each year, corresponding to 40 bursaries per each of the UTGSU’s three (3) Conference Bursary Cycles: Fall Cycle, Spring Cycle, and Summer Cycle. Applications to the 2018 UTGSU Conference Bursary (Fall Cycle) will open on November 1, 2018 and will remain open until 11:59 PM on November 15, 2018. This cycle is for conferences with start dates on or between December 1, 2018 and March 31, 2019. Please note that you must be a UTGSU Member at the time of application for your application to be deemed eligible. Applications will only be accepted for conferences yet to be attended, not for conferences already attended. Additionally, applicants may only submit one application per Conference Cycle. For more information and to access the Conference Bursary Application and Instructions please visit: https://www.utgsu.ca/funding/conference-bursary/ Contact Information and Accessibility If you require accessibility accommodations or have any questions related to the UTGSU Conference Bursary, please email the UTGSU Finance Commissioner at finance@utgsu.ca. ## Halloween 2018 ## Drop courses deadline – October 29, 2018 Drop courses absolute deadline: Monday, October 29, 2018 Students dropping courses on ACORN must also fill out a drop courses form and submit to the Graduate Office. http://www.sgs.utoronto.ca/Documents/Add+Drop+Courses.pdf Forms are also available on the counter in the math mailroom (BA 6290A). ## Departmental PhD Thesis Exam – Chia-Cheng Liu Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam. PhD Candidate: Chia-Cheng Liu Co-Supervisors: Joel Kamnitzer/Alexander Braverman Thesis title: A copy of the thesis can be found here: ## Halloween Tea and Costume Party There will be a special tea time on Halloween (Wednesday October 31) in the Department lounge at 2:00 pm. Costumes are encouraged, we will have prizes available for the best costumes. Halloween 2018 ## Departmental PhD Thesis Exam – Krishan Rajaratnam Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam. Friday, October 19, 2018 2:10 p.m. BA6183 PhD Candidate: Krishan Rajaratnam Supervisor: Michael Sigal Thesis title: Abrikosov lattice solutions of the ZHK Chern-Simons equations **** In this thesis we study the ZHK Chern-Simons equations which occur in the study of the fractional quantum hall effect of condensed matter physics. After stating basic properties of these equations, we first prove the existence of Abrikosov lattice solutions of them. Among these solutions, we find the physically interesting one whose lattice shape minimizes the average energy per lattice cell. In addition to the Abrikosov lattice solutions, we find solutions of the ZHK Chern-Simons equations on Riemann surfaces of higher genus$g$, by utilizing similar results for the Ginzburg-Landau equations. Finally, we study the orbital stability of the Abrikosov lattice solutions under perturbations which preserve the lattice. A copy of the thesis can be found here: ## Departmental PhD Thesis Exam – Steven Amelotte Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam. Tuesday, June 26 2018 1:10 p.m. BA6183 PhD Candidate: Steven Amelotte Supervisor: Paul Selick Thesis title: Unstable Homotopy Theory Surrounding the Fibre of the$p^\text{th}$Power Map on Loop Spaces of Spheres *** In this thesis, we study the fibre of the$p^\text{th}$power map on loop spaces of spheres with a view toward obtaining homotopy decompositions. For the prime$p=2$, we give an explicit decomposition of the fibre$\Omega^3S^{17}\{2\}$of the squaring map on the triple loop space of the$17$-sphere, building on work of Campbell, Cohen, Peterson and Selick, who showed that such decompositions are only possible for$S^5$,$S^9$and$S^{17}$. This induces a splitting of the mod$2$homotopy groups$\pi_\ast(S^{17}; \mathbb{Z}/2\mathbb{Z})$in terms of the integral homotopy groups of the fibre of the double suspension$E^2 \colon S^{2n-1} \to \Omega^2S^{2n+1}$and refines a result of Cohen and Selick, who gave similar decompositions for$S^5$and$S^9$. For odd primes, we find that the decomposition problem for$\Omega S^{2n+1}\{p\}$is equivalent to the strong odd primary Kervaire invariant problem. Using this unstable homotopy theoretic interpretation of the Kervaire invariant problem together with what is presently known about the$3$-primary stable homotopy groups of spheres, we give a new decomposition of$\Omega S^{55}\{3\}$. We relate the$2$-primary decompositions above to various Whitehead products in the homotopy groups of mod$2$Moore spaces and Stiefel manifolds to show that the Whitehead square$[i_{2n},i_{2n}]$of the inclusion of the bottom cell of the Moore space$P^{2n+1}(2)$is divisible by$2$if and only if$2n=2,4,8$or$16$. As an application of our$3$-primary decomposition, we prove two new cases of a longstanding conjecture which states that the fibre of the double suspension is a double loop space. A copy of the thesis can be found here: ut-thesis ## Departmental PhD Thesis Exam – Vincent Gelinas Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam. Monday, June 18, 2018 11:10 a.m. BA6183 PhD Candidate: Vincent Gelinas Co-Supervisors: Joel Kamnitzer, Colin Ingalls Thesis title: Contributions to the Stable Derived Categories of Gorenstein Rings *** Abstract: The stable derived category${\rm D}_{sg}(R)$of a Gorenstein ring$R$is defined as the Verdier quotient of the bounded derived category$ {\rm D}^b(\modsf R) $by the thick subcategory of perfect complexes, that is, those with finite projective resolutions, and was introduced by Ragnar-Olaf Buchweitz as a homological measure of the singularities of$R$. This thesis contributes to its study, centered around representation theoretic, homological and Koszul duality aspects. In Part I, we first complete (over$\C$) the classification of homogeneous complete intersection isolated singularities$R$for which the graded stable derived category${\rm D}^{\Z}_{sg}(R)$(respectively,$ {\rm D}^b(\coh X) $for$X = \proj R$) contains a tilting object. This is done by proving the existence of a full strong exceptional collection of vector bundles on a$2n$-dimensional smooth complete intersection of two quadrics$X = V(Q_1, Q_2) \subseteq \mathbb{P}^{2n+2}$, building on work of Kuznetsov. We then use recent results of Buchweitz-Iyama-Yamaura to classify the indecomposable objects in${\rm D}_{sg}^{\Z}(R_Y)$and the Betti tables of their complete resolutions, over$R_Y$the homogeneous coordinate rings of$4$points on$\mathbb{P}^1$and$4$points on$\mathbb{P}^2$in general position. In Part II, for$R$a Koszul Gorenstein algebra, we study a natural pair of full subcategories whose intersection$\mathcal{H}^{\mathsf{lin}}(R) \subseteq {\rm D}_{sg}^{\Z}(R)$consists of modules with eventually linear projective resolutions. We prove that such a pair forms a bounded t-structure if and only if$R$is absolutely Koszul in the sense of Herzog-Iyengar, in which case there is an equivalence of triangulated categories${\rm D}^b(\mathcal{H}^{\mathsf{lin}}(R)) \cong {\rm D}_{sg}^{\Z}(R)$. We then relate the heart to modules over the Koszul dual algebra$R^!$. As first application, we extend the Bernstein-Gel’fand-Gel’fand correspondence beyond the case of exterior and symmetric algebras, or more generally complete intersections of quadrics and homogeneous Clifford algebras, to any pair of Koszul dual algebras$(R, R^!)$with$R$absolutely Koszul Gorenstein. In particular the correspondence holds for the coordinate ring of elliptic normal curves of degree$\geq 4$and for the anticanonical model of del Pezzo surfaces of degree$\geq 4$. We then relate our results to conjectures of Bondal and Minamoto on the graded coherence of Artin-Schelter regular algebras and higher preprojective algebras; we characterise when these conjectures hold in a restricted setting, and give counterexamples to both in all dimension$\geq 4\$.

A copy of the thesis can be found here:  thesis

## Departmental PhD Thesis Exam – Huan Vo

Everyone is welcome to attend.  Refreshments will be served in the Math Lounge before the exam.

Wednesday, June 20 2018
11:10 a.m.
BA6183

PhD Candidate:  Huan Vo
Supervisor:   Dror Bar-Natan
Thesis title:  Alexander Invariants of Tangles via Expansions

****

Abstract:

In this thesis we describe a method to extend the Alexander polynomial to tangles. It is based on a
technology known as expansions, which is inspired by the Taylor expansion and the Kontsevich integral.
Our main object of study is the space of w-tangles, which contains usual tangles, but has a much simpler
expansion. To study w-tangles, we introduce an algebraic structure called meta-monoids. An expansion
of w-tangles together with a particular Lie algebra, namely the non-abelian two-dimensional Lie algebra,
gives us a meta-monoid called Γ-calculus that recovers the Alexander polynomial. Using the language
of Γ-calculus, we rederive certain important properties of the Alexander polynomial, most notably the
Fox-Milnor condition on the Alexander polynomials of ribbon knots [Lic97, FM66]. We argue that our
proof has some potential for generalization which may help tackle the slice-ribbon conjecture. In a sense
this thesis is an extension of [BNS13].

A copy of the thesis can be found here:  Thesis_HuanVo_V1

Over the last few years, the generosity of faculty, alumni and friends of the Department have allowed us to create a number of significant scholarships to support graduate students. This year’s winners are listed below.

1) Ida Bulat Memorial Graduate Fellowship:

Lennart Döppenschmitt (student of Marco Gualtieri)

2) Vivekananda Graduate Scholarship for International students:

Debanjana Kundu (student of Kumar Murty)

Saied Sorkhou (student of Joe Repka)

Mateusz Olechnowicz (student of Jacob Tsimerman, Patrick Ingram)