Calendar

TITLE: Noncommutative Geometry, the Spectral Aspect

ABSTRACT: This talk will be a survey of the spectral side of noncommutative geometry, presenting the new paradigm of spectral triples and showing its relevance for the fine structure of space-time, its large scale structure and also in number theory in connection with the zeros of the Riemann zeta function.

Talk chair: Peter Kronheimer

Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.”

For more information, please visit the event page.

Register here to attend.

TITLE: Subfactors–in Memory of Vaughan Jones

ABSTRACT: Jones initiated modern subfactor theory in early 1980s and investigated this area for his whole academic life. Subfactor theory has both deep and broad connections with various areas in mathematics and physics. One well-known peak in the development of subfactor theory is the discovery of the Jones polynomial, for which Jones won the Fields Metal in 1990. Let us travel back to the dark room at the beginning of the story, to appreciate how radically our viewpoint has changed.

Talk chair: Arthur Jaffe

Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.”

For more information, please visit the event page.

Register here to attend.

Derived categories and motives are important invariants of algebraic varieties invented by Grothendieck and his collaborators around 1960s. In 2005, Orlov conjectured that they will be closely related and now there are several evidences supporting his conjecture. On the other hand, moduli spaces of vector bundles on curves provide attractive and important examples of algebraic varieties and there have been intensive works studying them. In this talk, I will discuss derived categories and motives of moduli spaces of vector bundles on curves. This talk is based on joint works with I. Biswas and T. Gomez.

Zoom: https://harvard.zoom.us/j/91780604388?pwd=d3BqazFwbDZLQng0cEREclFqWkN4UT09

Multi-robot systems are already playing a crucial role in manufacturing, warehouse automation, and natural resource monitoring, and in the future they will be employed in even broader domains from space exploration to search-and-rescue. Moreover, these systems will likely be incorporated in our daily lives through drone delivery services and smart mobility systems that comprise of thousands of autonomous vehicles. The anticipated benefits of multi-robot systems are numerous, ranging from automating dangerous jobs, to broader societal facets such  as easing traffic congestion and sustainability. However, to reap those rewards we must develop control mechanisms for such systems that can adapt rapidly to unexpected changes on a massive scale. Importantly, these mechanisms must capture: (i) dynamical and collision-avoidance constraints of individual robots; (ii) interactions between multiple robots; and (iii) more broadly, the  interaction of those systems with the environment. All these considerations give rise to extremely complex and high-dimensional optimization problems that need to be solved in real-time.

In this talk I will present recent progress on the design of algorithms for  control and decision-making to allow the safe, effective, and societally-equitable deployment of multi-robot systems. I will highlight both results on fundamental capabilities for multi-robot systems (e.g., motion planning and task allocation), as well as applications in smart mobility, including multi-drone delivery and autonomous mobility-on-demand systems. Along the way, I will mention a few related open problems in mathematics and algorithm design.

BIO:
Kiril Solovey is roboticist specializing in multi-robot systems and their applications to smart mobility. He is currently a Postdoctoral Scholar at the Department of Aeronautics and Astronautics, Stanford University, working with Marco Pavone, where he is supported by the Center for Automotive Research (CARS). He obtained a PhD in Computer Science from Tel Aviv University, where he was advised by Dan Halperin.

Kiril’s research focuses on the design of effective control and decision-making mechanisms to allow multi-robot systems to tackle complex problems for the benefit of the society. His work draws upon ideas that span across the disciplines of engineering, computer science, and transportation science, to develop scalable optimization approaches with substantial guarantees regarding quality and robustness of the solution. For his work he received multiple awards, including the Clore Scholars and Fulbright Postdoctoral Fellowships, best paper awards and nominations (at Robotics: Science and Systems, International Conference on Robotics and Automation, International Symposium on Multi-Robot and Multi-Agent System, and European Control Conference), and teaching awards.

Zoom: https://harvard.zoom.us/j/98231541450

Multi-robot systems are already playing a crucial role in manufacturing, warehouse automation, and natural resource monitoring, and in the future they will be employed in even broader domains from space exploration to search-and-rescue. Moreover, these systems will likely be incorporated in our daily lives through drone delivery services and smart mobility systems that comprise of thousands of autonomous vehicles. The anticipated benefits of multi-robot systems are numerous, ranging from automating dangerous jobs, to broader societal facets such  as easing traffic congestion and sustainability. However, to reap those rewards we must develop control mechanisms for such systems that can adapt rapidly to unexpected changes on a massive scale. Importantly, these mechanisms must capture: (i) dynamical and collision-avoidance constraints of individual robots; (ii) interactions between multiple robots; and (iii) more broadly, the  interaction of those systems with the environment. All these considerations give rise to extremely complex and high-dimensional optimization problems that need to be solved in real-time.

In this talk I will present recent progress on the design of algorithms for  control and decision-making to allow the safe, effective, and societally-equitable deployment of multi-robot systems. I will highlight both results on fundamental capabilities for multi-robot systems (e.g., motion planning and task allocation), as well as applications in smart mobility, including multi-drone delivery and autonomous mobility-on-demand systems. Along the way, I will mention a few related open problems in mathematics and algorithm design.

BIO:
Kiril Solovey is roboticist specializing in multi-robot systems and their applications to smart mobility. He is currently a Postdoctoral Scholar at the Department of Aeronautics and Astronautics, Stanford University, working with Marco Pavone, where he is supported by the Center for Automotive Research (CARS). He obtained a PhD in Computer Science from Tel Aviv University, where he was advised by Dan Halperin.

Kiril’s research focuses on the design of effective control and decision-making mechanisms to allow multi-robot systems to tackle complex problems for the benefit of the society. His work draws upon ideas that span across the disciplines of engineering, computer science, and transportation science, to develop scalable optimization approaches with substantial guarantees regarding quality and robustness of the solution. For his work he received multiple awards, including the Clore Scholars and Fulbright Postdoctoral Fellowships, best paper awards and nominations (at Robotics: Science and Systems, International Conference on Robotics and Automation, International Symposium on Multi-Robot and Multi-Agent System, and European Control Conference), and teaching awards.

Zoom: https://harvard.zoom.us/j/98231541450

One possible interpretation of the SYZ conjecture is that for a polarized family of CY manifolds near the large complex structure limit, there is a special Lagrangian fibration on the generic region of the CY manifold. Generic here means a set with a large percentage of the CY measure, and the percentage tends to 100% in the limit. I will discuss my recent progress on this version of the SYZ conjecture, with emphasis on how differential geometers think about this problem, and give some hint about where nonarchimedean geometry comes in.

Zoom: https://harvard.zoom.us/j/96709211410?pwd=SHJyUUc4NzU5Y1d0N2FKVzIwcmEzdz09

TITLE: Theorems of Torelli type

ABSTRACT: Given a closed manifold of even dimension 2n, then Hodge
showed around 1950 that a kählerian complex structure on
that manifold determines a decomposition of its complex
cohomology. This decomposition, which can potentially vary
continuously with the complex structure, extracts from a non-linear
given, linear data. It can contain a lot of information. When there
is essentially no loss of data in this process, we say that the Torelli
theorem holds. We review the underlying theory and then survey
some cases where this is the case. This will include the classical
case n=1, but the emphasis will be on K3 manifolds (n=2) and
more generally, on hyperkählerian manifolds. These cases stand
out, since one can then also tell which decompositions occur.

Talk chair: Shing-Tung Yau

Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.”

For more information, please visit the event page.

Register here to attend.

Strongly correlated electron systems often show bad-metal behavior, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.

Zoom: https://harvard.zoom.us/j/977347126