Loading Events

« All Events

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 Webinar

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.

Directions to CMSA

Register Online for in-person talks

Register Online for Zoom Webinar

Confirmed Speakers:

  • Evgeniya Akhmedova, Weizmann Institute of Science
  • Nima Arkani-Hamed, IAS
  • Carolina Figueiredo, Princeton University
  • Yu-tin Huang, National Taiwan University
  • Dani Kaufmann, University of Copenhagen
  • Chia-Kai Kuo, National Taiwan University
  • Thomas Lam, University of Michigan
  • Yelena Mandelshtam, UC Berkeley
  • Elizabeth Pratt, UC Berkeley
  • Lecheng Ren, Brown University
  • Melissa Sherman-Bennett, MIT & UC Davis
  • Marcus Spradlin, Brown University
  • Ran Tesler, Weizmann Institute of Science
  • Hugh Thomas, Université du Québec à Montréal
  • Jaroslav Trnka, UC Davis
  • Anastasia Volovich, Brown University

Organizers:

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 cstillman@math.harvard.edu no later than Monday, April 15, 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

Wed, 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

Thu, 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

Fri, 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

 

About the image:

Left: the 3-dimensional associahedron, Fomin and Zelevinsky
Center: artistic depiction of the amplituhedron, Gilmore
Right: Schlegel diagram of a hypersimplex, Ziegler

Details

Start:
May 29, 2024 @ 9:00 am
End:
May 31, 2024 @ 5:00 pm
Event Category:

Venue

CMSA Room G10
CMSA, 20 Garden Street
Cambridge, MA 02138 United States
+ Google Map
Phone:
6174967132