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

TBA

BA6183

PhD Candidate: Travis Ens

Supervisor: Dror Bar-Natan

Thesis title:

***

A copy of the thesis can be found here:

Dec

03

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

TBA

BA6183

PhD Candidate: Travis Ens

Supervisor: Dror Bar-Natan

Thesis title:

***

A copy of the thesis can be found here:

Nov

01

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.

Oct

25

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).

Oct

25

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.

Jun

12

*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

May

29

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)

**3) Canadian Mathematical Society Graduate Scholarship**:

Saied Sorkhou (student of Joe Repka)

**4) Coxeter Graduate Scholarship**:

Mateusz Olechnowicz (student of Jacob Tsimerman, Patrick Ingram)

**5) International Graduate Student Scholarship**:

Abhishek Oswal (student of Jacob Tsimerman)

**6) Margaret Isobel Elliott Graduate Scholarship**:

Keegan Da Silva Barbosa (student of Stevo Todorcevic)

**7) Irving Kaplansky Scholarship**:

Jamal Kawach (student of Stevo Todorcevic)

Congratulations to all!

Apr

13

**A career panel for graduate students in mathematics
**

When: April 20, 2018

Where: BA6183

Time: 3:00-4:00 p.m.

*Reception and networking to follow in the graduate lounge.*

RSVP: https://doodle.com/poll/wbeb4rppg5vipuq4

**Panelists**

**Alex Bloemendal**:

Alex is a computational scientist at the Broad Institute of MIT and Harvard and at the Analytic and Translational Genetics Unit of Massachusetts General Hospital. As a member of Broad institute member Ben Neale’s lab, Alex leads a group in developing new methods to analyze genetic data, harnessing its unprecedented scope and scale to discover the genetic causes of disease. He also co-founded and directs the Models, Inference & Algorithms initiative at the Broad, bridging computational biology, mathematical theory, and machine learning. Alex is an institute scientist at the Broad. Alex was previously a research scientist in the Program for Evolutionary Dynamics and a Simons Fellow in the Department of Mathematics at Harvard University. His research in probability theory and random matrices focused on questions of signal and noise in high-dimensional data; he proved an open conjecture with wide-reaching applications for fields including population genetics. He also earned a teaching award for an advanced course on probability. Alex received an Hon. B.Sc., M.Sc., and Ph.D. in mathematics from the University of Toronto

**Aaron Chow:**

Aaron is a Senior Information Security Consultant – Security Engineering at CIBC. He graduated from our doctoral program in 2014.

**Dorian Goldman:
**Dorian develops mathematical models using modern methods in machine learning and statistics for Conde Nast. He’s also an Adjunct Professor of data science at Columbia University, where he’s teaching a course on using data science in industry which has received overwhelmingly positive reviews. He completed his MSc degree in mathematics at UofT and his PhDs at the Courant Institute (NYU) and UPMC (Paris VI) and worked full time as a research-only fellow and instructor of mathematics at DPMMS at the University of Cambridge. He worked in Germany, France, England and the USA over the past several years while completing his degrees and gained considerable experience in variational methods, differential equations and applied analysis. He transitioned into data science and machine learning three years ago, and became very passionate about the mathematical sophistication and significant impact that the field has.

**Diana Ojeda:**

Diana got her PhD in set theory at Cornell University and was a postdoc at U of T from 2014 to 2017. She now works as a SoC Engineer at Intel, developing modelling and analysis tools for FPGAs.

**Ben Schachter:**

Benjamin Schachter is a Consultant at the Boston Consulting Group, based in the Toronto office. He joined BCG full time in January 2018, after previously working at BCG as a summer Consultant in 2016. Ben has primarily worked in the technology, media, and telecommunications (TMT) practice area. Ben completed his PhD in mathematics at the University of Toronto in 2017; his research focused on optimal transport and the calculus of variations. Ben also holds an MSc in mathematics from the University of Western Ontario and an MA and BA (hons.), both in economics, from the University of Toronto.

Mar

24

The Department of Mathematics will be holding a posthumous degree award ceremony for

*Yuri Cher*

on Tuesday, March 28, 2017

at

10:30 a.m.

in

BA6183

40 St. George St.

~

Everyone is welcome to attend. Refreshments will be served in the Graduate Lounge.

Mar

09

The Department of Mathematics will hold a Memorial Service for our late graduate student, Yuri Cher, on **Tuesday, March 28, 2017 at 10:30 a.m.** in the Math lounge.

A remembrance book will be available in the main office the week of March 20.

We look forward to having you join us.

Oct

21

**Monday, October 24, 2016 **

York Cemetery and Funeral Centre

160 Beecroft Rd, North York

ON M2N 5Z5

Visitation: 11:00 a.m.-12:00 p.m.

Service: 12:00 – 1:00 p.m.

Burial: 1:00 p.m.