Amplituhedra, Cluster Algebras, and Positive Geometry
May 29, 2024 @ 9:00 am - May 31, 2024 @ 5:00 pm
Amplituhedra, Cluster Algebras, and Positive Geometry
Dates: May 29-31, 2024
Location: Harvard CMSA, 20 Garden Street, Cambridge MA 02138 & via Zoom
In recent years, a remarkable paradigm shift has occurred in understanding quantum observables in particle physics and cosmology, revealing their emergence from underlying novel mathematical objects known as positive geometries. The conference will center on the amplituhedron—the first and major example of a positive geometry. Building on the work of Lusztig and Postnikov on the positive Grassmannian, the physicists Arkani-Hamed and Trnka introduced the amplituhedron in 2013 as a geometric object that “explains” the so-called BCFW recurrence for scattering amplitudes in N = 4 super Yang Mills theory (SYM). Simultaneously, cluster algebras, originally introduced by Fomin and Zelevinsky to study total positivity, have been revealed to have a crucial role in describing singularities of N = 4 SYM scattering amplitudes. Thus, one can use ideas from quantum field theory (QFT) to connect cluster algebras to positive geometries, and in particular to the amplituhedron. Additionally, QFT can also be used to discover new examples of positive geometries. The conference will bring together a wide range of mathematicians and physicists both to draw new connections within algebraic combinatorics and geometry and to advance our physical understanding of scattering amplitudes and QFT.
The conference features: Introductory Lectures, an Open Problems Forum, Emerging Scholars Talks, and talks by experts in the fields.
The conference aims to actively engage and empower junior researchers and women, ensuring their integral presence and impactful contributions.
Register Online for in-person talks
Confirmed Speakers:
- Evgeniya Akhmedova, Weizmann Institute of Science
- Nima Arkani-Hamed, IAS
- Paolo Benincasa, MPI
- Nick Early, Weizmann Institute of Science
- Carolina Figueiredo, Princeton University
- Yu-tin Huang, National Taiwan University
- Dani Kaufman, University of Copenhagen
- Chia-Kai Kuo, National Taiwan University
- Thomas Lam, University of Michigan
- Yelena Mandelshtam, UC Berkeley
- Shruti Paranjape, UC Davis
- Elizabeth Pratt, UC Berkeley
- Lecheng Ren, Brown University
- Sebastian Seemann, KU Leuven
- Melissa Sherman-Bennett, MIT & UC Davis
- Marcus Spradlin, Brown University
- Ran Tessler, Weizmann Institute of Science
- Hugh Thomas, Université du Québec à Montréal
- Jaroslav Trnka, UC Davis
- Anastasia Volovich, Brown University
Organizers:
- Matteo Parisi, Harvard CMSA
- Lauren Williams, Harvard Mathematics
This event will be co-funded by the National Science Foundation.
Limited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register above and send an email to amplituhedra@cmsa.fas.harvard.edu no later than Friday, April 19, 2024.
Please include your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc, please include a copy of your CV.
Preliminary Schedule
| Wednesday, May 29, 2024 | |
| 8.45 – 9.00 am | Registration |
| 9.00 – 9.45 am | Introductory Lecture #1: The Amplituhedron |
| 9.45 – 10.30 am | Introductory Lecture #2: Cluster Algebras |
| 10:30 – 10.45 am | Coffee Break |
| 10.45 – 11.30 am | Introductory Lecture #3: Positive Geometries |
| 11.30 – 12.15 pm | Talk #1 |
| 12.30 – 2.00 pm | Lunch Break |
| 2.00 – 2.45 pm | Talk #2 |
| 2.45 – 3.30 pm | Talk #3 |
| 3.30 – 4.00 pm | Coffee Break |
| 4.00 – 4.45 pm | Talk #4 |
| 5.00 – 6.00 pm | Welcome Reception |
Thursday, May 30, 2024 |
|
| 9.00 – 10.00 am | Talk #5 |
| 10.00 – 10.30 am | Coffee Break |
| 10.30 – 11.15 am | Talk #6 |
| 11.30 – 12.15 om | Talk #7 |
| 12.30 – 2.00 pm | Lunch Break |
| 2.00 – 2.45 pm | Talk #8 |
| 2.45 – 3.30 pm | Talk #9 |
| 3.30 – 4.00 pm | Coffee Break |
| 4.00 – 5.30 pm | Open Problems Forum |
| 6.00 – 8.00 pm | Conference Dinner |
Friday, May 31, 2024 |
|
| 9.00 – 10.00 am | Talk #10 |
| 10.00 –10.30 am | Coffee Break |
| 10.30 – 12.40 pm | Emerging Scholars Talks |
| 10.30 – 10.50 am: Short Talk #1 | |
| 10.50 – 11.10 am: Short Talk #2 | |
| 11.10– 11.30 am: Short Talk #3 | |
| 11.30 – 11.40 am: Short break | |
| 11.40 – 12.00 pm: Short Talk #4 | |
| 12.00 – 12.20 pm: Short Talk #5 | |
| 12.20 – 12.40 pm: Short Talk #6 | |
| 12.40 – 2.00 pm | Lunch Break |
| 2.00 – 2.45 pm | Talk #11 |
| 2.45 – 3.30 pm | Talk #12 |
| 3.30 – 3.45 pm | Coffee Break |
| 3.45 – 4.30 pm | Talk #13 |
| 4.30 – 5.00 pm | Farewell Tea |
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