Description
Superschools focus on topics at the interface of Mathematics and Physics. Graduate students and early career researchers, from both Mathematics and Physics, are guided, in an intense week-long summer school, by the mentors.
String Theory revolutionized not just how we view the physical world but also how we view Mathematics. Conversely, through String Theory, many physicists first became acquainted with beautiful fields of Mathematics, like Algebraic Geometry. The cross pollination of insights and motivations between String Theory and Mathematics led to remarkable insights in both fields. The topic for the Superschool is Derived Categories in Algebraic Geometry and D-branes in String Theory.
The curriculum of the Superschool consisted of approximately 20 hour-long lecture topics developing the foundational ideas for Derived Categories and D-branes and converging to a proof that D-branes in topological type B form a category, which is equivalent to the Derived Category of Coherent Sheaves in the case of a σ-model and equivalent to the Derived Category of Factorizations for a Landau-Ginzburg model. All lectures were prepared and delivered by the participants with guidance from the mentors. Interspersed are mentor-guided discussion sessions.
Participants
Dori Bejleri (Brown) | Jirui Guo (Virginia Tech) | Kento Osuga (Alberta) | |
Jake Bian (UBC) | Chantelle Hanratty (Alberta) | Stephen Pietromonaco (UBC) | |
Nitin Chidambaram (Alberta) | Andrew Harder (Miami) | Eric Sharpe (Virginia Tech) | |
Minako Chinen (Alberta) | Richard Hughes (UT-Austin) | Alex Takeda (UC-Berkeley) | |
Colin Diemer (Alberta) | Nafiz Ishtiaque (Perimeter) | Mattia Talpo (UBC) | |
Blake Farman (USC) | Yijia Liu (Waterloo) | Rebecca Tramel (Illinois) | |
David Favero (Alberta) | Jeongseok Oh (KIAS) | Zhongyi Zhang (Columbia) | |
Nathan Grieve (New Brunswick) |
Schedule
Monday: July 18 | ||
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9:00 | Hanratty | Triangulated Categories |
10:15 | Chidambaram | Triangulated Categories, Derived Categories |
11:45 | Osuga | Closed String B-model |
2:30 | Chinen | Introduction to Quivers |
3:45 | Discussion | |
Tuesday: July 19 | ||
9:00 | Liu | Exceptional Collections and Semi-orthogonal Decompositions |
10:15 | Tramel | Stability Conditions |
11:45 | Pietromonaco | B-model and Derived Categories |
2:30 | Zhang | Introduction to Fukaya Categories |
3:45 | Discussion | |
Wednesday: July 20 | ||
9:00 | Hughes | Introduction to Mirror Symmetry |
10:15 | Bejleri | SYZ Mirror Symmetry |
11:45 | Talpo | Introduction to Toric Mirror Symmetry |
2:30 | Takeda | Differential Graded Categories |
3:45 | Discussion | |
Thursday: July 21 | ||
9:00 | Harder | Introduction to Homological Mirror Symmetry |
10:15 | Oh | Introduction to Enumerative Mirror Symmetry |
11:45 | Bian | Phases of GLSMs |
2:30 | Grieve | Introduction to Geometric Invariant Theory |
3:45 | Discussion | |
Friday: July 22 | ||
9:00 | Diemer | Birational Geometry, Derived Categories, Orlov's Theorem, VGIT |
10:15 | Ishtiaque | GLSMs and D-branes |
11:45 | Guo | LG Models and Matrix Factorizations |
Organizers
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