Two Brandeis Professors Receive 2017 Simons Fellowships

Bit threads in a holographic spacetime

Bit threads in a holographic spacetime

Two Brandeis professors have been awarded highly prestigious and competitive Simons Fellowships for 2017. Daniel Ruberman received a 2017 Simons Fellowship in Mathematics. Matthew Headrick was awarded a 2017 Simons Fellowship in Theoretical Physics. This is the first of two articles where each recipient’s award-winning research is described.

Matthew Headrick’s research studies the phenomenon of entanglement in certain quantum systems and its connection to the geometry of spacetime in general relativity. This very active area of research is the culmination of three developments in theoretical physics over the past 20 years.

First, in 1997, string theorists discovered that certain quantum systems involving a large number of very strongly interacting constituents — whose analysis would normally be intractable — are secretly equivalent to general relativity — a classical theory describing gravity in terms of curved spacetime — in a space with an extra dimension. For example, if the quantum system has two dimensions of space, then the general relativity has three; the phenomenon is thus naturally dubbed “holography”.

This equivalence between two very different-looking theories is incredibly powerful, and has led to much progress in understanding both strongly-interacting quantum systems and general relativity. However, it is still not fully understood how or precisely under what conditions such an equivalence holds.

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Simons Foundation funds Brandeis Math, Physics collaborations

In 2014, the Simons Foundation, one of the world’s largest and most prominent basic science philanthropies, launched an unprecedented program to fund multi-year, international research collaborations in mathematics and theoretical physics. These are $10M grants over four years, renewable, that aim to drive progress on fundamental scientific questions of major importance in mathematics, theoretical physics, and theoretical computer science. There were 82 proposals in this first round. In September 2015, two were funded. Both involve Brandeis.

Matthew Headrick (Physics) is deputy director of the Simons Collaboration It from Qubit, which involves 16 faculty members at 15 institutions in six countries. This project is trying from multiple angles to bring together physics and quantum information theory, and show how some fundamental physical phenomena (spacetime, black holes etc.) emerge from the very nature of quantum information. Fundamental physics and quantum information theory remain distinct disciplines and communities, separated by significant barriers to communication and collaboration. “It from Qubit” is a large-scale effort by some of the leading researchers in both communities to foster communication, education and collaboration between them, thereby advancing both fields and ultimately solving some of the deepest problems in physics. The overarching scientific questions motivating the Collaboration include:

  • Does spacetime emerge from entanglement?
  • Do black holes have interiors?
  • Does the universe exist outside our horizon?
  • What is the information-theoretic structure of quantum field theories?
  • Can quantum computers simulate all physical phenomena?
  • How does quantum information flow in time?

Bong Lian (Mathematics) is a member of the Simons Collaboration on Homological Mirror Symmetry, which involves nine investigators from eight different institutions in three countries. Mirror Symmetry, first discovered by theoretical physicists in late ‘80s, is a relationship between two very different-looking physical models of Nature, a remarkable equivalence or “duality” between different versions of a particular species of multidimensional space or shape (Calabi-Yau manifolds) that seemed to give rise to the same physics. People have been trying to give a precise and general mathematical description of this mirroring ever since, and in the process have generated a long list of very surprising and far-reaching mathematical predictions and conjectures. The so-called “Homological Mirror Symmetry Conjecture” (HMS) may be thought of as a culmination of these efforts, and Lian was a member of the group (including S.-T. Yau) that gave a proof of a precursor to HMS in a series of papers in the late ‘90s.

Lian and his Simons collaborators are determined to prove HMS in full generality and explore its applications. One consequence of HMS says that if one starts from a “complex manifold” (a type of even-dimensioned space that geometers have been studying since Riemann described the first examples in 1845), then all its internal geometric structures can in fact be described using a certain partner space, called a “symplectic manifold”. The latter type of space was a mathematical edifice invented to understand classical physics in the mid-1900s. This connection goes both ways: any internal geometric structure of the symplectic partner also has an equally compelling description using the original complex partner. No one had even remotely expected such a connection, especially given that the discoveries of the two types of spaces — complex and symplectic — were separated by more than 100 years and were invented for very different reasons. If proven true, HMS will give us ways to answer questions about the internal geometric structure of a complex manifold by studying its symplectic partner, and vice versa.

Proving HMS will also help resolve many very difficult problems in enumerative geometry that for more than a century were thought to be intractable. Enumerative geometry is an ancient (and until recently moribund) branch of geometry in which people count the number of geometric objects of a particular type that can be contained inside a space. Mirror symmetry and HMS have turned enumerative geometry into a new way to characterize and relate shapes and spaces.

Why do so many powers of 2 start with “1”?

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384 …

If you liked math in middle school, odds are that maybe you memorized the powers of two. But did you ever think about the fact that so many of them start with the digit “1”? Is there a reason for it? How would you go about stating the problem in more formal mathematical terms?

Dmitry Kleinbock from the Brandeis Math department explains in this Numberphile video:

Be sure to watch the extra content (below) for a slightly more technical, but still completely approachable, additional explanation, where the problem reduces to the so-called equidistribution property of irrational rotations of the unit circle.

Are there other numbers more likely to start with the digit “1”?  It’s pretty easy to convince yourself that there are.

IGERT Summer Institute – July 27 to August 7, 2015

IGERTBrandeis is hosting a two-week summer institute for graduate students in the mathematical sciences from July 27-August 7.  This will combine the annual summer institute of Brandeis’ Geometry and Dynamics IGERT program, with a sequel to the US-India Advanced Studies Institute on thermalization, held two years ago in Bangalore.

Topics:

  • Large deviation theory
  • Statistics of extreme events
  • The large N expansion in statistical and quantum physics
  • Statistical fluid dynamics
  • Quantum information and quantum gravity
  • Thermalization in Quantum Systems

Lecturers:

Sumit Das (U. Kentucky)
Chandan Dasgupta (IISC, Bangalore)
Rajesh Gopakumar (HRI, Allahabad and ICTS)
Alex Maloney (McGill University)
Satya Majumdar (LPTMS, Paris)
Sanjib Sabhapandit (Raman Research Institute, Bangalore)
Peter Weichman (BAE systems)

Organizers:

Albion Lawrence
Bulbul Chakraborty

Registration:

There will be no registration fee, but the venue will have limited capacity, so interested students should register by sending an email to Catherine Broderick (cbroderi@brandeis.edu) by July 4. Please list your affiliation, your year in graduate school, any publications, and the name of your PhD advisor.

Additional information can be found at www.brandeis.edu/igert/.

Ira Gessel Is Honored at May 8 Conference

gesselIra Gessel, the Theodore W. and Evelyn G. Berenson Professor of Mathematics, is retiring from Brandeis University after more than 30 years of teaching and research. During this time, he has made significant contributions to mathematics and the field of combinatorics. Additionally, he has provided invaluable assistance to both colleagues and students.

A conference was held on Friday May 8, 2015 that celebrated Ira’s contributions and featured the following speakers:

Andrew Gainer-Dewar (Hobart and William Smith College)
Kyle Petersen (DePaul University)
Richard Stanley (MIT)
Dennis Stanton (University of Minnesota)
Guoce Xin (Capital Normal University)

The conference was followed by a dinner in his honor.

BrandeisNow provides additional information.

Phi Beta Kappa Elects 51 Division of Science Students

Phi_Beta_Kappa_KeyThe Brandeis chapter of Phi Beta Kappa recently elected 97 new members. Of the 97, at least 51 undergraduate students are majors in the Division of Science (Biochemistry, Biological Physics, Biology, Chemistry, Computer Science, Mathematics, Neuroscience, Physics and Psychology).

Congratulations to the following new Phi Beta Kappa members from the Division of Science:

Biochemistry

Malia Barbra McAvoy
Yehonatan Otzar Meschede-Krasa
Juhee Park
Lior Rozhansky
Hanchen Zhao (double major with Chemistry)

Biological Physics

Abigail Rose Knecht

Biology

Ignatius Ang
Zachary Ian Fried
Jenna Leah Kahane
Ariel Jennifer Katz
Yang Li
Yixuan Liao
Alice Yuan Meng
Khang Vi Nguyen (double major with Chemistry)
Danielle Marie Quintin
Sarah Shin

Chemistry

Khang Vi Nguyen (double major with Biology)
Soobyung Park
Noam Isaac Saper
Hanchen Zhao (double major with Biochemistry)

Computer Science

Kenneth William Foner
Huy Quang Mai
Grady Berry Ward (double major in Mathematics)

Mathematics

Cameron Zhang Fen
Trevor Weiss Kafka
Linda Li
Huy Quang Mai
Stefan Stanojevic
Zhengyang Zhou
Daniel Jackson Kutner (double major in Physics)
Murielle Claire Tugendhaft
Grady Berry Ward (double major in Computer Science)

Neuroscience

Jessica Allison Haley (double major with Psychology)
Kiera Gillian Sarill (double major with Psychology)

 

Physics

Wei Zhong Goh
Stefan Stanojevic
Daniel Jackson Kutner

Psychology

Kyra Jordana Borenstein
Hannah Dvorah Caldwell
Nicole Danielle Cardona
Avi David Cohen
Annie Cui
Jason Michael Desimone
Emily Rose Friedman
Jonathan David Gilman
Clara Emily Gray
Cecilie Gromada
Sarah Jessica Hack-Chabot
Jessica Allison Haley (double major with Neuroscience)
Jessica Lynn Lieberman
Danielle Mizrachi
Emily April Mostow
Linda Sue Nakagawa
Talia Michelle Portal
Jenna Louise Rice
Kiera Gillian Sarill (double major with Neuroscience)
Aliza Naomi Shapiro

See full story on BrandeisNow.

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