## news

##### Department Profiles: Hakim J. Walker

Dr. Hakim Walker joined the Harvard Department of Mathematics as a preceptor in 2017. A graduate of Boston University and The George Washington University, he...

##### Barry Mazur Awarded 2022 Chern Medal

Mazur received the award for his work in topology, arithmetic geometry, and number theory, and for his leadership and generosity in shaping the next generation...

##### Mike Hopkins Gives Lecture at 2022 Abel Prize Celebration

Dr. Michael J. Hopkins, George Putnam Professor of Pure and Applied Mathematics and Harvard Department of Mathematics Chair, gave a lecture titled "The great wild...

See Older News

## announcements

##### Diving Into Math with Emmy Noether
September 10, 2022      4:30 pm
Diving Into Math with Emmy Noether A theatre performance about the life of one of history’s most influential mathematicians. When: Saturday, September 10, 2022 Panel...
See Older Announcements

## upcoming events

• August 26, 2022
9:00 am
via Zoom Video Conferencing

CMSA EVENT

• September 10, 2022
4:30 pm
Diving Into Math with Emmy Noether

ANNOUNCEMENTS, OTHER MATHEMATICS DEPARTMENT EVENTS, CMSA EVENT

• October 6, 2022 - October 7, 2022
CMSA Math Science Lectures in Honor of Raoul Bott

SEMINARS, CMSA EVENT

< 2022 >
July
«
»
Sun
Mon
Tue
Wed
Thu
Fri
Sat
June
June
June
June
June
1
2
3
4
5
6
7
• CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics

##### CMSA EVENTCMSA Quantum Matter in Mathematics and Physics

10:30 AM-12:30 PM
July 7, 2022

Kenichi Konishi will cover both Part I and Part II from 10:30am – 12:30pm.

Part I: Anomalies, dynamics and phases in strongly-coupled chiral gauge theories: recent developments

After many years of efforts, still very little is known today about the physics of strongly-coupled chiral gauge theories in four dimensions, in spite of an important role they might play in the physics of fundamental interactions beyond the standard  SU(3)xSU(2)xU(1) model. This is in stark contrast with the vectorlike gauge theories for which we have many solid results, thanks to some exact theorems, to the lattice simulation studies, to the Seiberg-Witten exact solution of N=2 supersymmetric gauge theories, and last, but not the least, to the real-world strong-interaction phenomenology and experimental tests of Quantum Chromodynamics.

The purpose of this seminar is to discuss the results of our recent efforts to improve the understanding of the strongly-coupled chiral gauge theories. Among the main tools of analysis are the consideration of anomalies.  We use both the conventional ’t Hooft anomaly-matching ideas, and new, more stringent constraints coming from the generalized anomalies involving some higher-form symmetries.  Also, the so-called strong anomalies, little considered in the context of chiral gage theories, are found to carry significant implications.

As the playground we study several classes of SU(N) gauge theories, the so-called Bars-Yankielowicz models, the generalized Georgi-Glashow models, as well as a few other simple theories with the fermions in complex, anomaly-free  representations of the color SU(N).

Color-flavor-locked dynamical Higgs phase and dynamical Abelianization, emerge, among others, as two particularly interesting possible phases the system can flow into in the infrared, depending on the matter fermion content of the model.

Part II: Quantum fluctuations, particles and entanglements: towards the solution of the Quantum Measurement Problem

The quantum measurement problems are revisited from a new perspective.  One of the main ideas of this work is that the basic entities of our world are various types of particles, elementary or composite. It follows that  each elementary process, hence each measurement process at its core, is a spacetime, pointlike, event.

Another key idea is that, when a  microsystem  $\psi$  gets into contact with the experimental device,  factorization of $\psi$ rapidly fails and entangled mixed states appear.

The wave functions for the microsystem-apparatus coupled systems for different measurement outcomes then lack overlapping spacetime support. It means that  the aftermath of each measurement is a single term in the sum: the fact  sometimes perceived as the “wave-function collapse”.

Our discussion leading to a diagonal density matrix shows how the information encoded in the wave function gets transcribed, via entanglement with the experimental device and environment, into the relative frequencies for various experimental results.

These results represent new, significant steps towards filling in the logical gaps in the standard interpretation based on Born’s rule, replacing it with a more natural one. Accepting objective reality of quantum fluctuations, independent of any experiments, and independently of human presence, one renounces for good  the idea that in a fundamental, complete theory of Nature the result of each single experiment must necessarily be predictable.

A few well-known puzzles such as the Schr\”odinger cat conundrum and the EPR paradox will be briefly revisited: they can all be naturally explained away.

8
9
10
11
12
13
14
• CMSA EVENT: CMSA Interdisciplinary Science Seminar: Topological and geometrical aspects of spinors in insulating crystals

##### CMSA EVENTCMSA Interdisciplinary Science Seminar: Topological and geometrical aspects of spinors in insulating crystals

9:00 AM-10:00 AM
July 14, 2022

Introducing internal degrees of freedom in the description of crystalline insulators has led to a myriad of theoretical and experimental advances. Of particular interest are the effects of periodic perturbations, either in time or space, as they considerably enrich the variety of electronic responses. Here, we present a semiclassical approach to transport and accumulation of general spinor degrees of freedom in adiabatically driven, weakly inhomogeneous crystals of dimensions one, two and three under external electromagnetic fields. Our approach shows that spatio-temporal modulations of the system induce a spinor current and density that is related to geometrical and topological objects — the spinor-Chern fluxes and numbers — defined over the higher-dimensional phase-space of the system, i.e., its combined momentum-position-time coordinates.

The results are available here: https://arxiv.org/abs/2203.14902

Bio: Ioannis Petrides is a postdoctoral fellow at the School of Engineering and Applied Sciences at Harvard University. He received his Ph.D. from the Institute for Theoretical Physics at ETH Zurich. His research focuses on the topological and geometrical aspects of condensed matter system

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

15
16
17
18
19
20
21
• CMSA EVENT: CMSA Interdisciplinary Science Seminar: Infants’ sensory-motor cortices undergo microstructural tissue growth coupled with myelination

##### CMSA EVENTCMSA Interdisciplinary Science Seminar: Infants’ sensory-motor cortices undergo microstructural tissue growth coupled with myelination

9:00 AM-10:00 AM
July 21, 2022

The establishment of neural circuitry during early infancy is critical for developing visual, auditory, and motor functions. However, how cortical tissue develops postnatally is largely unknown. By combining T1 relaxation time from quantitative MRI and mean diffusivity (MD) from diffusion MRI, we tracked cortical tissue development in infants across three timepoints (newborn, 3 months, and 6 months). Lower T1 and MD indicate higher microstructural tissue density and more developed cortex. Our data reveal three main findings: First, primary sensory-motor areas (V1: visual, A1: auditory, S1: somatosensory, M1: motor) have lower T1 and MD at birth than higher-level cortical areas. However, all primary areas show significant reductions in T1 and MD in the first six months of life, illustrating profound tissue growth after birth. Second, significant reductions in T1 and MD from newborns to 6-month-olds occur in all visual areas of the ventral and dorsal visual streams. Strikingly, this development was heterogenous across the visual hierarchies: Earlier areas are more developed with denser tissue at birth than higher-order areas, but higher-order areas had faster rates of development. Finally, analysis of transcriptomic gene data that compares gene expression in postnatal vs. prenatal tissue samples showed strong postnatal expression of genes associated with myelination, synaptic signaling, and dendritic processes. Our results indicate that these cellular processes may contribute to profound postnatal tissue growth in sensory cortices observed in our in-vivo measurements. We propose a novel principle of postnatal maturation of sensory systems: development of cortical tissue proceeds in a hierarchical manner, enabling the lower-level areas to develop first to provide scaffolding for higher-order areas, which begin to develop more rapidly following birth to perform complex computations for vision and audition.

This work is published here: https://www.nature.com/articles/s42003-021-02706-w

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

22
23
24
25
26
27
28
• CMSA EVENT: CMSA Interdisciplinary Science Seminar: Statistical Mechanical theory for spatio-temporal evolution of Intra-tumor heterogeneity in cancers: Analysis of Multiregion sequencing data

##### CMSA EVENTCMSA Interdisciplinary Science Seminar: Statistical Mechanical theory for spatio-temporal evolution of Intra-tumor heterogeneity in cancers: Analysis of Multiregion sequencing data

9:00 AM-10:00 AM
July 28, 2022

Variations in characteristics from one region (sub-population) to another are commonly observed in complex systems, such as glasses and a collection of cells. Such variations are manifestations of heterogeneity, whose spatial and temporal behavior is hard to describe theoretically. In the context of cancer, intra-tumor heterogeneity (ITH), characterized by cells with genetic and phenotypic variability that co-exist within a single tumor, is often the cause of ineffective therapy and recurrence of cancer. Next-generation sequencing, obtained by sampling multiple regions of a single tumor (multi-region sequencing, M-Seq), has vividly demonstrated the pervasive nature of ITH, raising the need for a theory that accounts for evolution of tumor heterogeneity. Here, we develop a statistical mechanical theory to quantify ITH, using the Hamming distance, between genetic mutations in distinct regions within a single tumor. An analytic expression for ITH, expressed in terms of cell division probability (α) and mutation probability (p), is validated using cellular-automaton type simulations. Application of the theory successfully captures ITH extracted from M-seq data in patients with exogenous cancers (melanoma and lung). The theory, based on punctuated evolution at the early stages of the tumor followed by neutral evolution, is accurate provided the spatial variation in the tumor mutation burden is not large. We show that there are substantial variations in ITH in distinct regions of a single solid tumor, which supports the notion that distinct subclones could co-exist. The simulations show that there are substantial variations in the sub-populations, with the ITH increasing as the distance between the regions increases. The analytical and simulation framework developed here could be used in the quantitative analyses of the experimental (M-Seq) data. More broadly, our theory is likely to be useful in analyzing dynamic heterogeneity in complex systems such as supercooled liquids.

29
30
• CONFERENCE: Advances in Mathematical Physics: A Conference in Honor of Elliott H. Lieb on his 90th Birthday.

##### CONFERENCEAdvances in Mathematical Physics: A Conference in Honor of Elliott H. Lieb on his 90th Birthday.

All day
July 30, 2022-August 1, 2022

A Conference in Honor of Elliott H. Lieb on his 90th Birthday

Dates: July 30-August 1, 2022

Harvard University

July 30 – 31, 2022: Hall B, Science Center, 1 Oxford Street, Cambridge, MA, 02138
August 1, 2022: Hall C, Science Center, 1 Oxford Street, Cambridge, MA, 02138

Register Here

Conference Schedule

Saturday, July 30, Hall B

Sunday, July 31, Hall B

Monday, August 1, Hall C

8:45 a.m. – 9 a.m.

Refreshments

8:45 a.m. – 9 a.m.

Refreshments

8:45 a.m. – 9 a.m.

Refreshments

9 a.m. – 9:45 a.m.

Jan Philip Solovej

9 a.m. – 10 a.m.

Hugo Duminil-Copin

9 a.m. – 9:45 a.m.

Yoshiko Ogata

9:45 a.m. – 10:30 a.m.

László Erdös

10 a.m. – 10:30 a.m.

Tea Break

9:45 a.m. – 10:30 a.m.

Hal Tasaki

10:30 a.m. – 11 a.m.

Tea Break

10:30 a.m. – 11:15 a.m.

Jürg Fröhlich

10:30 a.m. – 11 a.m.

Tea Break

11 a.m. – 11:45 a.m.

Robert Seiringer

11:15 a.m. – 12 p.m.

Bertrand Halperin

11 a.m. – 11:45 a.m.

Bruno Nachtergaele

11:45 a.m. – 12:30 p.m.

Rupert Frank

12:00 p.m. – 1:30 p.m.

Lunch

11:45 a.m. – 12:30 p.m.

Alessandro Guiliani

12:30 p.m. – 2 p.m.

Lunch

1:30 p.m. – 2:15 p.m.

Jun Yin

12:30 p.m. – 2 p.m.

Lunch

2 p.m. – 2:45 p.m.

Simone Warzel

2:15 p.m. – 3 p.m.

Sabine Jansen

2 p.m. – 2:45 p.m.

Ron Peled

2:45 p.m. – 3:30 p.m.

Benjamin Schlein

3 p.m. – 3:30 p.m.

Tea Break

2:45 p.m. – 3:30 p.m.

Mathieu Lewin

3:30 p.m. – 4 p.m.

Tea Break

3:30 p.m. – 4:30 p.m.

A Review of Lieb’s Work

3:30 p.m. – 4 p.m.

Tea Break

4 p.m. – 4:45 p.m.

Rafael Benguria

4 p.m. – 4:45 p.m.

Eric Carlen

Organizers:
Michael Aizenman, Princeton University
Joel Lebowitz, Rutgers University
Ruedi Seiler, Technische Universität Berlin
Herbert Spohn, Technical University of Munich
Horng-Tzer Yau, Harvard University
Shing-Tung Yau, Harvard University
Jakob Yngvason, University of Vienna

Speakers:
Rafael Benguria, Pontificia Universidad Catolica de Chile
Eric Carlen, Rutgers University
Philippe Di Francesco, University of Illinois
Hugo Duminil-Copin, IHES
László Erdös, Institute of Science and Technology Austria
Rupert Frank, The California Institute of Technology
Jürg Fröhlich, ETH Zurich
Alessandro Giuliani, Università degli Studi Roma Tre
Bertrand Halperin, Harvard University
Klaus Hepp, Institute for Theoretical Physics, ETH Zurich
Sabine Jansen, Ludwig Maximilian University of Munich
Mathieu Lewin, Université Paris-Dauphine
Bruno Nachtergaele, The University of California, Davis
Yoshiko Ogata, University of Tokyo
Ron Peled, Tel Aviv University
Benjamin Schlein, University of Zurich
Robert Seiringer, Institute of Science and Technology Austria
Jan Philip Solovej, University of Copenhagen
Hal Tasaki, Gakushuin University
Simone Warzel, Technical University of Munich
Jun Yin, The University of California, Los Angeles

31
• CONFERENCE: Advances in Mathematical Physics: A Conference in Honor of Elliott H. Lieb on his 90th Birthday.

##### CONFERENCEAdvances in Mathematical Physics: A Conference in Honor of Elliott H. Lieb on his 90th Birthday.

All day
July 31, 2022-August 1, 2022

A Conference in Honor of Elliott H. Lieb on his 90th Birthday

Dates: July 30-August 1, 2022

Harvard University

July 30 – 31, 2022: Hall B, Science Center, 1 Oxford Street, Cambridge, MA, 02138
August 1, 2022: Hall C, Science Center, 1 Oxford Street, Cambridge, MA, 02138

Register Here

Conference Schedule

Saturday, July 30, Hall B

Sunday, July 31, Hall B

Monday, August 1, Hall C

8:45 a.m. – 9 a.m.

Refreshments

8:45 a.m. – 9 a.m.

Refreshments

8:45 a.m. – 9 a.m.

Refreshments

9 a.m. – 9:45 a.m.

Jan Philip Solovej

9 a.m. – 10 a.m.

Hugo Duminil-Copin

9 a.m. – 9:45 a.m.

Yoshiko Ogata

9:45 a.m. – 10:30 a.m.

László Erdös

10 a.m. – 10:30 a.m.

Tea Break

9:45 a.m. – 10:30 a.m.

Hal Tasaki

10:30 a.m. – 11 a.m.

Tea Break

10:30 a.m. – 11:15 a.m.

Jürg Fröhlich

10:30 a.m. – 11 a.m.

Tea Break

11 a.m. – 11:45 a.m.

Robert Seiringer

11:15 a.m. – 12 p.m.

Bertrand Halperin

11 a.m. – 11:45 a.m.

Bruno Nachtergaele

11:45 a.m. – 12:30 p.m.

Rupert Frank

12:00 p.m. – 1:30 p.m.

Lunch

11:45 a.m. – 12:30 p.m.

Alessandro Guiliani

12:30 p.m. – 2 p.m.

Lunch

1:30 p.m. – 2:15 p.m.

Jun Yin

12:30 p.m. – 2 p.m.

Lunch

2 p.m. – 2:45 p.m.

Simone Warzel

2:15 p.m. – 3 p.m.

Sabine Jansen

2 p.m. – 2:45 p.m.

Ron Peled

2:45 p.m. – 3:30 p.m.

Benjamin Schlein

3 p.m. – 3:30 p.m.

Tea Break

2:45 p.m. – 3:30 p.m.

Mathieu Lewin

3:30 p.m. – 4 p.m.

Tea Break

3:30 p.m. – 4:30 p.m.

A Review of Lieb’s Work

3:30 p.m. – 4 p.m.

Tea Break

4 p.m. – 4:45 p.m.

Rafael Benguria

4 p.m. – 4:45 p.m.

Eric Carlen

Organizers:
Michael Aizenman, Princeton University
Joel Lebowitz, Rutgers University
Ruedi Seiler, Technische Universität Berlin
Herbert Spohn, Technical University of Munich
Horng-Tzer Yau, Harvard University
Shing-Tung Yau, Harvard University
Jakob Yngvason, University of Vienna

Speakers:
Rafael Benguria, Pontificia Universidad Catolica de Chile
Eric Carlen, Rutgers University
Philippe Di Francesco, University of Illinois
Hugo Duminil-Copin, IHES
László Erdös, Institute of Science and Technology Austria
Rupert Frank, The California Institute of Technology
Jürg Fröhlich, ETH Zurich
Alessandro Giuliani, Università degli Studi Roma Tre
Bertrand Halperin, Harvard University
Klaus Hepp, Institute for Theoretical Physics, ETH Zurich
Sabine Jansen, Ludwig Maximilian University of Munich
Mathieu Lewin, Université Paris-Dauphine
Bruno Nachtergaele, The University of California, Davis
Yoshiko Ogata, University of Tokyo
Ron Peled, Tel Aviv University
Benjamin Schlein, University of Zurich
Robert Seiringer, Institute of Science and Technology Austria
Jan Philip Solovej, University of Copenhagen
Hal Tasaki, Gakushuin University
Simone Warzel, Technical University of Munich
Jun Yin, The University of California, Los Angeles

August
August
August
August
August
August