*On November 9, 2020, the Simons Center for Geometry and Physics (SCGP) celebrated its 10th anniversary with a special symposium and luncheon at the Center. The SCGP was officially founded in 2008 and the physical building’s inauguration was on November 9, 2010. Thus, this special commemoration marked ten years from the opening of the brick-and-mortar building. It was a memorable day with insightful reflections on the scientific and historical events that led to the creation of a Center for advancement at the nexus of geometry and theoretical physics.*

The decennial celebration took place in the Della Pietra Family Auditorium as well as in the Center’s atrium and gallery. Moderated by Luis Álvarez-Gaumé, Director of the SCGP, it was in tune with our times as a hybrid event with some guests in attendance at the Center and most participants attending via Zoom. Álvarez-Gaumé introduced Stony Brook University President Maurie McInnis, and Simons Foundation President Marilyn Simons, both providing tributes to the University and the SCGP. President McInnis spoke about collaboration as one of Stony Brook’s defining characteristics and honored the Center’s success in bringing geometry and physics together. She stated: “Collaboration is deep in the core of what we do—from our interdisciplinary perspective to our incredibly special relationship with our community, to our integrated, cutting-edge research. We want to be on the forefront of breakthrough scientific discovery. We want to not only respond, but help shape and define the world around us. […]The Simons Center for Geometry and Physics is a shining example of our success in doing just that.”

Marilyn Simons spoke next and commended the Simons Center for “bringing together the greatest minds in mathematics and physics to expand our understanding of the fundamental nature of our universe. The beauty of the ideas here are so well reflected in the beauty of the building itself; the architectural design, the umbilic torus, the iconic wall—all over, it’s stunning.” She graciously praised the Center for engaing visitors “not only with its art, but its newsletter and its events, and people are invited here […]to come, and to and contemplate the creativity and the wonder of the human mind.” Accolades and candid remarks were also provided by the Chair of the SCGP Board of Trustees Yakov Eliashberg (Stanford) and by Cumrun Vafa (Harvard), former Chair of the Board.

Historical and scientific talks followed remarking upon the seeds planted for the Center long ago in the many collaborative and intellectual exchanges that took place over the decades between Stony Brook’s mathematicians and theoretical physicists. A thorough review of the highlights of mathematics research at the SCGP was presented by John Morgan, founding Director of the SCGP. Nathan Seiberg (IAS) provided an outside perspective highlighting the theoretical physics research at the SCGP. Martin Roček (YITP), one of the founders and organizer of the Simons Summer Workshops, talked about the Workshops’ history and role in the creation and development of the Center. And Alexander (Sasha) Abanov, SCGP Deputy Director, spoke about the history and structure of the SCGP’s multitude of programs and workshops.

Nigel Hitchin (Oxford), an emeritus member of the SCGP Board of Trustees, reminisced about the SCGP’s official opening and its early planning stages. Regarding the role of Research Assistant Professors, he recollected how it was agreed to create “an atmosphere of talking and listening, benefiting from both sides and sets of intuition,” as this is where ideas between mathematics and physics come together. “This is an important role the Center plays.” He also mentioned the life of Galileo, who was forced to quarantine for weeks due to the plague of the 1630s before being put on trial for heresy by the Inquisition. We are reminded of the COVID pandemic of 2020.

George Sterman (Director of the YITP and a member of the SCGP Board of Trustees) discussed the role of the Center as a research institute, comparing it to “an ivory tower with open discussions and open doors,” which, after 10 years, “under the guidance of John, and of Luis, is among Stony Brook’s signature contributions to scientific research.”

Scientific talks were given by the four SCGP permanent faculty members: Simon Donaldson (mathematics), Kenji Fukaya (mathematics), Zohar Komargodski (physics), and Nikita Nekrasov (physics). Other distinctive lectures were provided by Juan Maldacena (IAS), and Andrei Okounkov (Columbia), both members of the SCGP Board of Trustees. Their outlook talks presented exciting discoveries and the leading role the Simons Center plays in geometry and physics that evidences a promising future.

Luis Álvarez-Gaumé concluded the celebration by announcing the Center’s many plans for the next ten years. “A decade from now, we will have a better perspective to assess the achievement fostered by the SCGP. I am quite certain we will be looking back in awe and grateful for the success story of this collaboration between the Simons Center and Stony Brook University.”

Jim Simons’ closing remarks succinctly summed up a life’s experience for the realization of a Center that fuses mathematics, physics, and all the permeations thereof, for a space where discovery and imagination ignite: “When I came to Stony Brook to be the Chair of the Math Department…I began to realize that physics, or at least a lot of physics, and mathematics, were inextricably bound together…and could flourish, even better perhaps, if there were a place where mathematicians and physicists were working together.”

*The Simons Center for Geometry and Physics was founded with a generous gift from Jim and Marilyn Simons. For more on the Center’s founding and history, please, see SCGP News Volume XV: Special 10th Anniversary Edition, pages 34–47.*

Download the article HERE!

]]>Download the article HERE!

]]>*Since 1978, the Wolf Foundation awards the acclaimed, international Wolf Prize to outstanding scientists and artists from around the world. In 2020, the Wolf Prize in Mathematics was awarded jointly to Yakov Eliashberg (Stanford) and Simon Donaldson (SCGP). In this article, Kenji Fukaya shares his thoughts on the awardees esteemed contributions to differential geometry and topology.*

As one of the founders of global symplectic geometry, Yakov Eliashberg has been a leader in this field for the past 40 years. The field of symplectic geometry studies mechanics (Hamiltonian mechanics) from the geometric point of view. This area itself is very classical, but recently people found that non-trivial global symplectic geometry also exists. Importantly, among many different kinds of geometries, global geometry is rarely non-trivial

The existence of global symplectic geometry was established via a certain remarkable result by Eliashberg. Soon after this was determined, Mikhael Gromov introduced the method of pseudo-holomorphic curve. Since then, global symplectic geometry has been one of the most active areas of mathematics.

Eliashberg also obtained many basic results in contact geometry—an odd dimensional cousin of symplectic geometry. Together with Helmut Hofer and Alexander Givental, Eliashberg also proposed Symplectic Field Theory, which associates highly sophisticated algebraic structure to a contact manifold. This conjecture is now being established by mathematicians of a younger generation such as Bao-Honda, Pardon and Ishikawa.

Eliashberg’s recent research is on the flexibility of symplectic geometry. The existence of global symplectic geometry means that certain objects cannot exist in a symplectic world. The flexibility means that certain objects do exist in a symplectic world. It is ideal that we know exactly the borderline between a rigid world and a flexible world. For a long time this was a dream far from reality. New work by Eliashberg (together with his younger collaborators such as Murphy) shows that the world of symplectic geometry is more flexible than we thought before. So now we are closer to the dream.

Sir Simon Donaldson is one of the most accomplished researchers of geometry in the last 50 years. When he was just in his 20s, Donaldson found an astonishing result on 4-dimensional topology. Topologists had used linear differential equations for a long time in their research. Donaldson found that by using a certain non-linear differential equation—Yang-Mills equation—we can prove that 4-dimensional Euclidean space has an ‘exotic’ smooth structure. When this result appeared many topologists wondered whether this was a sporadic result or not. Donaldson then solved many fundamental open questions on differential topology of 4-manifolds by using Yang-Mills equation. Since then Gauge theory (such as Yang-Mills equation) plays the dominant role in the study of differential topology of 4-dimensional manifo

Donaldson also gave a fundamental contribution to symplectic geometry. Gromov discovered that one can use a complex analytic map from complex one-dimensional space to a symplectic manifold as a tool to study symplectic manifolds. On the other hand, complex analytic function on a symplectic manifold does not exist generically. Donaldson nevertheless showed we can still study symplectic manifolds by using ‘almost’ complex analytic function.

Donaldson’s recent important achievement focuses on the existence of Einstein metric on complex manifolds. One of the most important results in geometric analysis (by Yau) is the existence of Kähler metric with Ricci curvature 0 (that is, a solution of Einstein’s equation of gravity) under a certain easily checkable assumption. There is a similar result by Audin and Yau in the case of negative Ricci curvature. The case of positive Ricci curvature has long been a standing open question. Donaldson, together with his collaborators Sun and Chen, finally solved this problem.

*Congratulations to Yakov Eliashberg and Simon Donaldson on their ground-breaking contributions in geometry and topology.*

The Della Pietra Lecture Series commenced in 2011 with a generous donation from the Della Pietra families. The series aims to bring world-renowned scientists to the Simons Center for Geometry and Physics to enhance the intellectual activity of the Center and bring greater awareness of recent and impactful discoveries in physics and mathematics.

In December 2019, the Center was honored to host Dr. Manjul Bhargava to deliver a set of very inspiring Della Pietra lectures. Over the course of several days, Bhargava presented three lecturers: one for the general public, a second for local high school students, and a third, more technical talk, for the mathematics and the physics communities at Stony Brook.

Bhargava is the R. Brandon Fradd Professor of Mathematics at Princeton University, and the Stieljes Professor of Number Theory at Leiden University. He also holds an Adjunct Professorship at the TIFR in Mumbai, and the University of Hyderabad. Bhargava has been assisting the Indian government in designing programs for learning mathematics, and he has spent extended periods in India. We were fortunate to have the opportunity to welcome him during a brief window between two trips to Delhi.

Primarily known for his contributions to number theory, Bhargava has received numerous awards for his work, in particular the Fields Medal in 2014, “for developing powerful new methods in the geometry of numbers which he applied to count rings of small rank and to bound the average rank of elliptic curves.”

Bhargava’s technical talk, “How Likely it is for an Integer Polynomial to Take a Square Value,” began with the history of a problem that has fascinated mathematicians since antiquity—the understanding of whether a mathematical expression takes a square value. Starting from simple results, some dating back hundreds of years, he blazed his path with cutting edge results in current research in number theory. The audience was enthralled by his remarkable communication skills, through which he was able to effortlessly illuminate an understanding of the nuts and bolts of contemporary deep theorems.

For Bhargava’s high school lecture, which took place in spite of the first major snowstorm, the Della Pietra auditorium was at full capacity. This was most fortunate as the Center also introduced a new special event preceding the talk. Students were received by faculty and SCGP members for one ambitious hour of math and physics discovery. They were divided into small groups to engage in discussion and presentations with senior and junior researchers. We counted on the presence of Senior Professors Moira Chas, Alexander Kirillov, Sasha Abanov, Simon Donaldson, Zohar Komargodski, Peter van Nieuwenhuizen, Sam Grushevsky, Luis Álvarez-Gaumé, and Art Director Lorraine Walsh with Research Assistant Professors Catherine Cannizzo, Luigi Tizzani, Rodrigo Barbosa, for demonstrations and tours.

These interactions with the students were quite interesting, and also a warmer way to welcome them to the scientific community, even if for a brief visit. And the Center’s *Iconic Wall *provided a good opportunity to break the ice across generations.

After meeting faculty, the students were ushered into the auditorium for Bhargava’s lecture “Patterns in Numbers and Nature.” The talk explored the multitude of beautiful patterns found in the world around us. Patterns in tilings, the numbers of petals in daisies, the spiral structures on pine cones, the emergence of cicadas into the sunlight every 17 years, and how many such patterns lead to the study of deep structures in mathematics. As a number theorist, most of the research is concentrated in the study of a deceptively simple universe, that of whole numbers: 1 2 3 4 5 6 7 8 … It is very easy to ask questions in simple terms that turn out to be extraordinarily deep, and have no answer (yet) in such a seemingly simple structure. They range from questions that appear as mathematical games to problems in the very foundations of mathematics itself.

Bhargava has a rather eclectic palette of interests, including classical music and Sanskrit poetry. Sanskrit poems feature a mix of short and long syllables that last for one or two beats respectively. As a child, he was interested in understanding how many different rhythms it is possible to construct with a given number of beats. Bhargava discovered the answer in a treatise on poetry, the Chandahsastra, written by Pingalla more than two thousand years ago. There is a simple formula, the number of rhythms with n beats is equal to the number of rhythms with n-1 beats, plus those with n-2. There are known as the Hemachandra numbers (named for the 11th century scholar Acharya Hemachandra who wrote about them). These were discovered in Western mathematics later, and are known as

Fibonacci numbers, or as the Fibonacci sequence. This sequence is at the root of the fundamental golden ratio that is ubiquitous in art, architecture, and in nature, and with an appropriate measure rep- resents the most irrational of all irrational numbers.

The interactions with the high school students and our community were dynamic and productive. We look forward to continuing this expanded outreach. And we hope to host Dr. Manjul Bhargava and his mother Mira (a mathematician herself, and his first real professor of mathematics) in the not too distant future. The Center remains grateful to the Della Pietra families for the unwavering support they provide, and also for sponsoring this remarkable series of lectures. •

]]>By Abhay Deshpande, Professor, Stony Brook University; Director, EIC Science, Brookhaven National Laboratory

**Recent news and excitement**

On January 9, 2020, the US Department of Energy (DOE) announced the selection of Brookhaven National Laboratory (BNL) as the site of its future Electron Ion Collider (EIC). The EIC will be built over the next ten years with an estimated cost between $1.6 and $2.6 billion. With this announcement ended a two-decade long phase of making the scientific case for the collider within the broader science community: The Nuclear Science Advisory Committee’s Long Range Planning discussions in 2002, 2007 and 2015 [1], an independent assessment of the EIC science by the National Academy of Science, Engineering & Medicine (NAS) in October 2018 [2] followed by official start of the project (Critical Decision 0) within the Office of Science in December 2019, and finally, the site selection in January 2020. EIC realization begins with BNL and Jefferson Lab working closely together with the DOE and the potential EIC Users Group to realize its science in the 2030’s.

The visible universe is made of atoms of various naturally occurring elements. At the heart of the atom are nuclei, made of protons and neutrons (collectively called hadrons). Electrons fly around these nuclei in well-defined and well understood orbits. The interactions amongst the electrons and the nuclei are mediated by photons, the carriers of the electroweak force – an extremely well understood force of nature. Photons themselves are chargeless. They can only interact with *electrically* charged particles, such as protons, neutrons and other electrons, but can’t interact with other photons.

Inside the hadrons is the realm of strong interactions, mediated by the force carrier called the “gluon”. Gluons are also massless, and electrically neutral but carry a novel “color” charge, which enables them to interact not only with the colored quarks and antiquarks but also *amongst themselves*. This ability of gluon *self-interaction* leads to profoundly important consequences. A color charge in isolation can initiate gluon radiation, and due to its ability to self-interact, lead to an uncontained growth in gluon number resulting in a

“thundercloud” [3]. Nature controls this by confining color inside hadrons with finite energy, tames this growth and prevents the thundercloud. Such color interactions lead to the incredible richness and complexity of the strong interactions.

Quantum Chromodynamics (QCD), the theory of strong interactions within the Standard Model of Physics, is unquestionably the right theory that describes the interactions amongst partons (quarks and gluons) inside the hadrons. The 2004 Nobel Prize in Physics was awarded to David Gross, H. David Politzer and Frank Wilczek “for their discovery of asymptotic freedom in the theory of strong interactions” within the framework of QCD, and yet many fundamental and compelling questions related to gluon’s role in QCD remain unanswered. Without gluons there would be no hadrons, no atomic nuclei, no galaxies—no visible matter. The Higgs Boson which is often credited for imparting “mass” to the universe, actually provides less than 1% of the mass of the visible universe. The rest comes from the partonic interactions, including in large part driven by gluons. How this happens exactly is not understood, but astonishingly, the massless gluons and almost massless quarks, through their interactions make up the entire visible matter and its mass in the Universe. Precision study of the gluon and their interaction is hence called “the next QCD frontier” [4].

Using the precision enabled by the well understood electroweak force the EIC will study the quark-gluon structure and their dynamics in the hadrons and in nuclei with unprecedented precision. EIC is the only collider ever designed to collide polarized electrons with polarized protons, deuterons, and a few light nuclei and with all stable nuclei over a broad range of center of mass energies. This makes the EIC one of *the most technically demanding* accelerator facilities in the world. In the National Academy’s consensus report [2], it was hence noted that the EIC would not only help maintain U.S. leadership in nuclear physics, but also in the accelerator science and technology.

**The Science Opportunities at the Electron Ion Collider**

**Origin of Mass and Spin**

Most of the mass of the visible universe comes from the protons and neutrons in the nuclei of the atoms. Electrons themselves contribute very little. Protons and neutrons are made of almost massless quarks, antiquarks and the massless gluons. Together they contribute to barely 2% of the protons mass. Where does the rest of the mass come from? It is expected that the motion of quarks and the energy of the gluons resulting from their *interactions *must contribute in the total relativistic energy of the system contributing to the remaining 98% of the proton’s mass, see Figure 2 (Right). Exactly how this happens remains a mystery.

Nucleon’s spin is similarly an enigma. Quarks are fermions (spin ½ particles) and gluons are bosons (spin 1). Their spin alignment was until recently expected to contribute and explain the entire spin of a nucleon. However, experiments at CERN, SLAC and DESY in the late 1980’s, and the 1990’s revealed that in fact, quarks and anti-quarks together only contribute about 25% of the nucleon spin. In 2000’s the PHENIX and STAR experiments at RHIC with polarized protons have revealed that the gluon-spin contribution to the nucleon’s spin also seems to be about 25%. Where does the remaining 50% spin of the nucleon come from? Experimental evidence of transverse motion of quarks and anti-quarks inside the nucleon leads to the picture of quarks and anti-quarks having orbital motion) in the sea of gluons. Those orbital momenta collectively should contribute to the nucleon’s total angular momentum explaining the total the nucleon spin (Figure 2: Right). The same relativistic motion of quarks and gluons naturally explain origin of the mass of the nucleon. A direct measurement and observation of orbital motion of quarks and gluons is needed. A detailed and systematic study of direct measurement of this orbital motion by studying the spatial and momentum correlations of quarks and gluons is one of the most important goals of the EIC [4].

**Novel Cold Dense Gluonic Matter**

Nuclei are accurately modeled as collection colorless protons and neutrons interacting with each other through long range forces mediated by the exchange of pions. There is another regime predicted in QCD at high energy where quarks become static sources of gluon fields reaching extreme high density. The EIC would be able to experimentally investigate this high energy regime of QCD employing electron scattering off high energy protons and heavy nuclei which are known to have very large number of gluons. The HERA collider (the high energy e-p collider that operated at DESY 1992-2006) found that the number of gluons grows exponentially inside the protons at high energy. In nuclei, a significantly higher gluon densities are expected than in protons at the comparable energies. The gluons in the nuclei are expected to overlap in the transverse position inside the nuclei and reach a highly dense quantum state of “cold dense gluonic matter”. This novel state, often called the “Color Glass Condensate (CGC)” could be the QCD analogue of the Bose-Einstein Condensate of cold atoms studied in atomic physics. To experimentally measure this effect, we would use nuclei at the highest possible energy available at the EIC, and shine the virtual light originating from high energy electron as shown in Figure 3.

Figure 3 shows a schematic of a quark-antiquark dipole in DIS colliding with a high energy nucleus enabling gluon exchange. A process identical to “diffraction of mono-chromatic light off an opaque object” is expected to occur due to the highly dense gluonic object formed in nuclei at high energies, resulting in a “diffraction pattern” in particle production. A large fraction of e-A scattering will be channeled into such diffractive scattering should such “wall of glue” exist. Experiments at HERA saw *hints *of such effect. The high density of gluons possible using the nuclear beams at the highest energy, the EIC will decisively produce robust signatures of CGC if it exists.

**Color Interactions in Nuclei, Hadronization**

Figure 4 shows a schematic of the parton moving through the nucleus after being kicked by the virtual photon emitted from the electron. The parton must *neutralize its color* by picking up appropriate partners as it passes through the nucleus. This color neutralization process results in the formation of color neutral mesons (called “hadronization”) detected in the detector. At high enough energies, a “jet” of color charged particles (instead of a single charge) could be traversing through the nucleus. The EIC and an appropriately designed detector would enable detailed studies of hadronization by exquisite control over energy and the amount of the nuclear medium by controlling the size of the nucleus.

**The Electron Ion Collider at Brookhaven National Laboratory**

The layout of the EIC at BNL is shown in Figure 5. The EIC will require addition of a 5-18 GeV electron storage ring in the existing RHIC tunnel to collide with protons and ions. Polarized electrons will be created in the source (shown in red) and accelerated before injection into the electron injector and then into the turquoise electron storage ring. The electrons and the ions could collide at two possible locations of future detectors. The center of mass range for the EIC electron ion collisions will range from 30-140 GeV for electron-proton scattering and up to 100 GeV for electron-ion collisions. The electrons will be polarized, and so will the protons and a few light ions. All possible stable nuclei starting from the proton to Uranium will be provided by the Electron Beam Ionization Source (EBIS).

Intensity of the beams in collision results in a quantity called the Luminosity of a collider. Luminosity in units of *“# of collisions/unit-area/unit-time”* is used to address the number of events the experimenters would see. At the EIC, the desired range of luminosity for its planned physics program is 1033-34 cm-2sec-1. This is 100-1000 times larger than the highest luminosity achieved by an of electron-proton collider ever. These ranges of luminosity and energy of the collider along with the physics goals are summarized in Figure 6. Also shown are two machine performance curves that could be delivered at two interaction regions optimized for different Center of Mass energies.

**Connections to Other Fields of Physics (selected highlights)**

**EIC and High Energy Physics**

EIC will be a frontier high luminosity facility, with unprecedented potential for achieving high precision. Beyond the Standard Model, enthusiasts are looking into high sensitivity experimental searches for novel physics signals in the EIC’s energy range. The high luminosity of EIC will provide significantly improved flavor separated parton distribution functions (PDFs) and transverse momentum distribution (TMDs) functions. After the Luminosity Upgrade of LHC, the EIC-improved PDFs will be essential for new physics searches at the LHC.

**EIC and Lattice QCD**

While QCD itself is impossible to solve exactly [5] for various reasons, a discretized version of QCD, in which space and time coordinates become points on a four-dimensional lattice (Lattice-QCD or LQCD) can be solved exactly given enough computing power. Extraction of physics results from LQCD involves limitations due to the finite size of the lattice and the extrapolations to the continuum limit. However, calculations do yield results with possibility of estimating their uncertainties reliably. Recently novel methods have been developed to calculate Quasi-PDFs, and then related them to true PDFs through iterative calculations employing established theoretical tools of Effective Field Theory (EFT) [5]. By the time the EIC will start producing precision data on nucleon spin and related observables, it is anticipated that the novel LQCD tools will also be ready to calculate them with comparable precision, ensuring a new era in QCD studies. LQCD could potentially become the standard tool to interpret the measurements at the EIC and potentially also guide its future program.

**EIC and Condensed Matter Physics**

At the high energy end of the spectrum of measurements, the EIC will study new types of many-body phenomena, namely the saturation in gluonic matter. At RHIC and LHC, the saturated gluonic state of matter is expected to be present for a short time before it decays into the Quark Gluon Plasma (QGP). It is proposed that the decay of the gluonic matter into the QGP seeds formation of topological defects resulting in the handedness in quark-antiquark pair formation, recently seen in heavy ion collisions, called the “chiral magnetic effect” (CME). Analogues of CME have been seen in condensed matter physics. The initialization of topological defects in heavy ion collisions depends on the details of the color field in saturated gluonic matter whose discovery and study is a central experimental goal of the EIC. With the recent rapid progress in condensed matter physics of novel topological materials suggests possibility of interactions between QCD at the EIC and condensed matter physics to continue in the future.

**EIC and Accelerator Physics**

Several novel accelerator technologies have been incorporated into the EIC’s design. They serve as intellectual challenges attracting the best of the accelerator scientists to the EIC. Exciting opportunities exist in demonstrating and implementing strong hadron beam cooling necessary to achieve the highest of luminosities. A combination of stochastic cooling and the novel Coherent electron Cooling (CeC) are being developed. Other challenging technologies that will be pushed to their state-of-the-art include superconducting RF, Crab Cavities, those needed to mitigate electron clouds, strong focusing magnets for interaction regions, spin rotators for manipulating beam spin orientation and development of high current polarized sources for electrons and light ions.

**A Collider Facility in our Backyard**

The physics program at the EIC will be carried out by a worldwide community of nuclear physicists. The EIC user group boasts 1000+ users from 31 countries and is expected to grow by at least a factor of two by the time it operates. The EIC will be the only collider in the US and will operate for ~20 years. With enormously challenging machine parameters it will be a magnet for the brightest of minds in nuclear and accelerator physics research. The proximity of Stony Brook University to BNL is sure to serve both institutions extremely well in attracting scientists interested in the EIC.

It is quite natural that having a major facility in the proximity of a university influences the opportunities available to the faculty, post-docs and students enormously. It is a particular blessing for undergraduate student researchers enabling them to be actively involved in research even while taking classes. Research fields associated with such facilities naturally become strong at the University. The RHIC at BNL impacted the nuclear physics group (one of the top ranked group in nuclear physics the country) over the past two decades. Having the EIC in Stony Brook University’s backyard will ensure this for the next few decades.

The Center for Frontiers in Nuclear Science (CFNS) [6] was established in September 2017 jointly by Stony Brook and BNL, supported by funds from the Simons Foundation and NY State. CFNS has so far focused on supporting EIC science and young scientists involved in the EIC. In a very short time, it established itself as a world-leading Center for EIC science. CFNS currently runs an annual program of international workshops, topical meetings, a visitor program, a post-doctoral fellow program, an annual international summer school and a seminar series. Annually the Center hosts ~300 scientists through such activities. In the EIC era the Center assures an intellectually exciting environment at Stony Brook University. The vision for CFNS is to become a world-leading Center for EIC & broader nuclear science by growing its scope to other frontiers areas in nuclear science, and to the education & support of minorities. •

References

[1] Nuclear Science Advisory Committee (NSAC) Long Range Planning Reports 2002, 2007, 2015; Explicit link: https://science.osti.gov/np/nsac

[2] National Academies of Sciences, Engineering and
Medicine. 2018. *An Assessment of U.S.-Based Electron Ion Collider Science. *Washington
DC: The National Academies Press. https://doi.org/10.17226/25171.

[3] *Asymptotic Freedom: From Paradox to Paradigm*,
Frank Wilczek, Nobel Prize Lecture, December 8, 2004; https://www.nobelprize.org/uploads/2018/06/wilczek-lecture.pdf

[4] *Electron Ion Collider: the Next QCD Frontier –
Understanding the glue that binds us all*, A. Accordi et al, Eur. Phus. J. A
52 (2016) 9, 268 Editors: A. Deshpande, Z.-E. Meziani & J.-W. Qiu;
arXiv:1212.1701v3 [nucl-ex]

[5] *Parton physics on a Euclidean lattice*, X. Ji,
Phys. Rev. Lett. 110.262002

[6] Center for Frontiers in Nuclear Science (CFNS) http://www.stonybrook.edu/cfns

]]>To watch the video, please visit: http://scgp.stonybrook.edu/video/video.php?id=4493

An excerpt, as published in SCGP News Vol XIV, can be found below:

**ZK:** Congratulations on becoming the first Research Associate Professor at the Simons Center! Very well deserved. We have a few questions for you now. When and why did you become interested in physics?

**MM:** I became interested in physics in high school, around junior year. I had long been interested in math, but in high school, math was somewhat easy, and I had a physics teacher who, whenever he had a good day, taught really challenging things and posed really challenging problems. Basically, it was the challenge physics problems posed that got me interested. And then came the book by Brian Greene, *The Elegant Universe. *My mom’s boss, an American, gifted it to me and I read it. It was fascinating and got me really interested in fundamental physics. Then I started reading popular books.

**ZK: **How was your English at that point?

**MM:** I knew enough English to read that book. I learned it at school and after-school programs. By that time, I was pretty good, not so much in speaking but in reading.

**ZK:** Then you participated in the Physics Olympiad?

**MM:** Yes. The challenging problems led to the Physics Olympiads, which are taken very seriously in Hungary. There were weekly preparations taking place in my high school, for all of Budapest. Everybody who was interested in physics problems came to this after-school two-hour weekly club, including from the Hungarian-speaking parts of Slovakia. It was a big deal. They took the train for two hours just to participate in it. And there were fun problems—not really Olympiad-style which are boring and long—but tricky, fun ones.

**ZK:** In my time they also used to be short and tricky but now they are boring and long.

**MM:** Yes, the fun ones were tricky, Russian-style or Hungarian-style problems. And then we always got a long problem sheet that we had to solve for the following week—somebody presented it and it was a lot of fun. So, there were these preparations for the Olympiad, and I did it for two years. And that’s how I learned physics, really, on the high school level.

**ZK: **Do you remember some particular puzzles from that time that you still think are beautiful or worth sharing?

**MM: **I might not remember the solution.

**ZK:** That’s fine, we can look up the solution.

**MM: **One that was really fun was to estimate or give a dimensional analysis type of an equation for the time it takes for sand to run through an hourglass, as a function of different parameters of the hourglass. This question seems very hard at first. It’s amazing that you can answer it based on dimensional analysis. There seems to be so many parameters. I think the trick is that you shouldn’t include the size of the grains of sand in your dimensional analysis.

**ZK:** Very nice. In your more recent career, you have written a few seminal papers on the connection between some ideas in high energy and condensed matter physics, such as quantum criticality, and various kinds of black holes. Can you speak to us about what are the most important lessons from the work that you have done for black hole physics, and what are the most important lessons for condensed matter physics?

**MM:** The underlying ideology behind much of my work is to use AdS/CFT or Gauge/Gravity duality, which is an exact equivalence between gravitational theories and strongly correlated quantum many-body systems. The idea behind applying this framework to problems in strongly coupled physics is that you ask what kind of phenomena are generic in the gravitational system, which might provide interesting or surprising dynamical phenomena in the many-body language. So, my work on quantum criticality and black holes was driven by the realization that there are generic black holes in string theory, which have a certain kind of geometry, and this geometry implies or predicts some exotic phenomena in strongly coupled systems, e.g., scaling symmetry in the time direction, but fairly local physics in space. We are used to critical points where space and time play similar roles. In these types of examples, their roles are very dissimilar because in time you have very long correlations, but in space, very short ones. And such phenomenological models have been written down in condensed matter before. But the fact that this is so generic in gravity was a realization that we made. We speculated that this represents some universal intermediate energy liquid-like phase of matter that might be somewhat generic in strongly coupled systems.

**ZK:** What is the gravitational dual of this?

**MM: **These are AdS_{2} throats with some transverse space. And this work I did in the early 2010s and

recently…

**ZK:** The correlations are local in space, so you can reduce some space and it is just quantum mechanics?

**MM:**The way the physics works is that in the time direction the scaling exponents are dependent on the wave number in the transverse space, so it’s somewhat dependent on the spatial structure. The way to visualize it is these clusters next to each other that are only coupled in some way that the correlation length is finite. So, that’s almost individual clusters but they still talk to each other.

**ZK:** It’s like stacks of things in space.

**MM:** Yes. But AdS_{2} physics kind of made the reappearance recently in the context of this SYK model. And a good model of these phases would be to consider SYK models coupled to each other in some spatially local way. I’ve been following this recent work on AdS_{2} because of my past with these phases.

**ZK:** More recently you also contributed a lot of work to the subject that goes by the name* T**T* deformations. Can you tell us a little bit about why that’s interesting and what are the main questions in that field?

**MM:** There are two reasons, somewhat independent, for why *T**T* is interesting. One—it provides the first example known to me where you start from a long-distance infrared description of physics, then you learn a little bit of the remnants of the UV physics, the technical term is that you know what irrelevant operator appears in the low energy, long distance effective action. And just from this information you can reconstruct the microphysics and learn what the ultraviolet behavior of the system is. This would be completely out of question in one of the familiar examples of a

non-trivial… Renormalization group flow here in the theory of strong interactions at long distances we have some theory of mesons and perhaps baryons and in terms of those degrees of freedom it seems completely infeasible that you would be able to describe the microphysics of quarks and gluons. But then in *T**T*, at least in one way of thinking about it, just knowing the infrared degrees of freedom and that you are working with this very special theory, you can learn about the microphysics.

**ZK:**What people did in real life was they observed hadrons, i.e., mesons, baryons and they reconstructed the quarks. In fact, they sort of actually did that.

**MM: **Well. But then they didn’t just do very low energy experiments. To discover partons they really had to go through…

**ZK:** Yes, a hypothesis based on low energy experiments.

**MM:** Correct. But then the dynamics of quarks and gluons was really only revealed by high energy scattering. Is that fair?

**ZK:**I think so, yes.

**MM: **That is one reason why *T**T* is interesting and the other reason again comes from the connection between gravitational theories and strongly coupled systems. And that is where we, with Lauren McGough and Herman Verlinde, made a proposal for what the gravitational dual, gravitational equivalent description of the *T**T* deformation might be in two-dimensional boundary theories/three-dimensional pure gravity. And the prescription is that you implement a sharp cut-off on the bulk geometry at finite distance and impose Dirichlet boundary conditions. This prescription produces gravitational physics that is mirrored in the field theory in the *T**T* deformation. Thus, we have this very nice holographic theory of quantum gravity, but it’s very hard to reconstruct local gravitational physics from it. And so our proposal is an interesting step in that direction where you can “detach” yourself from the asymptotic boundary and study more local bulk physics. This has generated a lot of interest in the field and people are trying to exploit this new way of thinking about local bulk physics. It’s a deformation of the boundary theory by an irrelevant operator.

**ZK:** So the bulk physics doesn’t exist before you do the deformation?

**MM:** It does exist. It’s encoded in a very nonlocal way in the boundary degrees of freedom. And by doing these deformations you can make the encoding somewhat simpler.

**ZK: **So you’re saying that the holographic information is encoded more obviously?

**MM:** Yes.

**ZK:** What a wonderful creation! Last question. Do you have any advice for researchers of your age and stage on how to work out the work-life balance, especially if people have young children? You have been tremendously, as they say nowadays, “productive.” Perhaps you can share with us your experience on how to strike a healthy balance between work and family life?

**MM:** If you look at my pattern of publications you will notice that when my son was born it went down drastically for at least half a year and then it picked up again. Some of my recent productivity is basically just projects that were started before my son was born and are just being finished. I mean, one important advice is not to kill yourself. As probably every parent knows, during the first half-year you are just a zombie. So you can’t do much about it. You should accept it. And when you get your energy levels back you can catch up. One nice thing in theory is that even if you missed some time, some months, a year, you can get back into it. It’s not like working in a lab where your mice die or your bacteria don’t evolve. It’s very easy to get back into research. And the other thing that was very helpful for me is to start working more extensively with collaborators who are perhaps younger, perhaps students who can do some calculations that you would also be able to do, but you don’t have enough time. So for me it was, I think, broadening a little bit the pool of people that I collaborate with was certainly helpful.

**ZK:** Well, you seem to have recently collaborated extensively with some students at Stony Brook. Was it useful?

**MM:** Yes, I found it very useful for the reason I talked about. I think I have enough experience that I can see what problems are feasible and then the students can be extremely useful in figuring out the details. And there are some excellent students in Stony Brook, so it’s very helpful. Yes.

**ZK:** Very good. Thanks so much for the interview!

**MM:** Thank you. •

Assistant Professor of Physics

C.N. Yang Institute for Theoretical Physics

Stony Brook University

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]]>I met Professor Eugenio Calabi in the Fall of 1989, a couple of months after I arrived on the University of Pennsylvania campus. We hit it off quite nicely, as he was a zealous lecturer and loved to go to the blackboard, while I was an eager listener and loathed to go in front of people, for fear that they might find out that I was not as good as my transcripts might have indicated. In retrospect, he must have found out early on, in his infinite wisdom, that I didn’t understand much of what he was talking about, but that apparently didn’t dampen an iota of his enthusiasm for talking to me. In my recollection, we spent 4-5 hours each day “talking” mathematics to each other—be it in his office, in the mailroom, or in our tea room. This is extraordinary luck for any graduate student to be blessed with. I endured growing pains for a long period of time after my graduation and Professor Calabi was with me during the whole process. His wit, humor and focus on the fundamentals have helped me regain balance in shaky times, and keep cool in sunny times. I cherish his invaluable teachings and wish to share these with the community. What follows are a few dialogues we have had over the years which hopefully will help elucidate the lasting wisdom of Eugenio Calabi.

**Like any ambitious young person, I was
curious about how to be famous:**

**XC:** How many papers do I need to write in order to be famous?

**EC:** One.

**Eugenio Calabi stresses the importance of
being original and doing what you love: **

**XC:** It seems to be relatively easy to write papers on a trendy subject?

**EC:** Be original and follow your own heart and

intuition.

**XC:** How do I be original?

**EC:** Read classical papers which have withstood the test of time. Like a dog, smell the smell miles away before anyone else has noticed.

**I often complained about the hardship
of getting my papers published: **

**XC:** Will being in a famous university help publish my papers?

**EC:** Maybe. Do you want your address to become famous because of you, or you to become famous

because of your address?

**XC:** A mediocre paper gets published in a top journal, what should I do?

**EC:** Nothing. If your paper is of fundamental importance, people would find it even if it were published in the corner of earth; if your paper is of mediocre quality, you are better off to be published in an obscure journal so no one will notice it.

**When I was relatively young, I was shocked to find out that a friend had “cheated” on me. It was a tough pill to swallow, but Calabi steered me away from bitterness: **

**XC: **A friend has stolen my idea. What should I do?

**EC:** Congratulations, now your idea is worth stealing!

**XC:** ???

**EC:** Will you have new ideas?

**XC:** Yes.

**EC:** Will you allow him to steal again?

**XC:** No.

**EC:** Then you win since you continue to have new ideas and he cannot continue to steal from you.

**For many, including myself, going to ICM is an ego trip. Calabi helped put it into perspective: **

**XC:** I was invited to ICM 2002.

**EC:** Congratulations, it is important to you personally!

**XC:** Just personally?

**EC:** Yes. We will know if it is important to geometry in 10 years. Think about who you remember among ICM speakers in differential geometry in 1994 or earlier.

Ever since my student years, Eugenio Calabi has stressed to me over and over again that it is mathematical problems, not he, that is my teacher. I didn’t quite understand initially, but I have gradually gained an appreciation and become a faithful follower of his philosophy. Indeed, with limited talent myself, I was blessed with many extremely gifted students and hence opportunities to put his philosophy into practice. We find good problems together and learn mathematics from the problems we work on. As a side benefit, I have learned, though with some struggles, quite a bit from my students over the years. Calabi is correct that problems and gifted students are my teachers. This is the biggest secret of my moderately successful career and I wish to share it with future generations.

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