- 2203/22/2022
Swampland Program
Please visit the Swampland Initiative for current events.
The Harvard Swampland Initiative is an immersive program aiming to bring together leading experts with the goal of exploring the boundaries of the quantum gravity landscape. Through workshops, seminars, and collaborative research, participants collectively navigate the Swampland, advancing our comprehension of the fundamental principles of quantum gravity.
During the 2021-2022 academic year, the CMSA hosted a program on the so-called “Swampland.”
The Swampland program aims to determine which low-energy effective field theories are consistent with nonperturbative quantum gravity considerations. Not everything is possible in String Theory, and finding out what is and what is not strongly constrains the low energy physics. These constraints are naturally interesting for particle physics and cosmology, which has led to a great deal of activity in the field in the last few years.
The Swampland is intrinsically interdisciplinary, with ramifications in string compactifications, holography, black hole physics, cosmology, particle physics, and even mathematics.
This program will include an extensive group of visitors and a slate of seminars. Additionally, the CMSA will host a school oriented toward graduate students.
Seminars
Swampland Seminar Series & Group Meetings
Program Visitors
- Pieter Bomans, Princeton, 10/30/21 – 11/02/21
- Irene Valenzuela, Instituto de Física Teórica, 02/14/22 – 02/21/22
- Mariana Grana, CEA/Saclay, 03/21/22 – 03/25/22
- Hector Parra De Freitas, IPHT Saclay, 03/21/22 – 04/01/22
- Timo Weigand, 03/21/22 – 03/28/22
- Gary Shiu, University of Wisconsin-Madison, 04/03/22 – 04/10/22
- Thomas van Riet, Leuven University, 04/03/22 – 04/09/22
- Lars Aalsma, University of Wisconsin-Madison, 04/11/22 – 04/15/22
- Sergio Cecotti, 05/08/22 – 05/21/22
- Tom Rudelius, 05/09/22 – 05/13/22
https://sites.harvard.edu/swampland-initiative/
Flip processes
Abstract: We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself ($k$ is fixed). The process starts with a given $n$-vertex graph $G_0$. In each step, the graph $G_i$ is obtained by sampling $k$ random vertices $v_1,\ldots,v_k$ of $G_{i-1}$ and replacing the induced graph $F:=G_{i-1}[v_1,\ldots,v_k]$ by $\mathcal{R}(F)$. This class contains several previously studied processes including the Erd\H{o}s–R\’enyi random graph process and the triangle removal process.
Given a flip process with a rule $\mathcal{R}$, we construct time-indexed trajectories $\Phi:\Gra\times [0,\infty)\rightarrow\Gra$ in the space of graphons. We prove that for any $T > 0$ starting with a large finite graph $G_0$ which is close to a graphon $W_0$ in the cut norm, with high probability the flip process will stay in a thin sausage around the trajectory $(\Phi(W_0,t))_{t=0}^T$ (after rescaling the time by the square of the order of the graph).
These graphon trajectories are then studied from the perspective of dynamical systems. Among others, we study continuity properties of these trajectories with respect to time and the initial graphon, existence and stability of fixed points and speed of convergence (whenever the infinite time limit exists). We give an example of a flip process with a periodic trajectory. This is joint work with Frederik Garbe, Matas \v Sileikis and Fiona Skerman (arXiv:2201.12272).
We also study several specific families flip processes. This is joint work with Pedro Ara\’ujo, Eng Keat Hng and Matas \v{S}ileikis (in preparation).
A brief introduction to the necessary bits of the theory of graph limits will be given in the talk.General Relativity Program Minicourses
CMSA, 20 Garden Street, Cambridge, MA 02138 USAMinicourses
General Relativity Program Minicourses
During the Spring 2022 semester, the CMSA hosted a program on General Relativity.
This semester-long program included four minicourses running in March, April, and May; a conference April 4–8, 2022; and a workshop from May 2–5, 2022.
Schedule Speaker Title Abstract March 1 – 3, 2022
10:00 am – 12:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.Dr. Stefan Czimek Characteristic Gluing for the Einstein Equations Abstract: This course serves as an introduction to characteristic gluing for the Einstein equations (developed by the lecturer in collaboration with S. Aretakis and I. Rodnianski). First we set up and analyze the characteristic gluing problem along one outgoing null hypersurface. Then we turn to bifurcate characteristic gluing (i.e. gluing along two null hypersurfaces bifurcating from a spacelike 2-sphere) and show how to localize characteristic initial data. Subsequently we turn to applications for spacelike initial data. Specifically, we discuss in detail our alternative proofs of the celebrated Corvino-Schoen gluing to Kerr and the Carlotto-Schoen localization of spacelike initial data (with improved decay). March 22 – 25, 2022
22nd & 23rd, 10:00 am – 11:30am ET
24th & 25th, 11:00 am – 12:30pm ETLocation: Hybrid. CMSA main seminar room, G-10.Prof. Lan-Hsuan Huang Existence of Static Metrics with Prescribed Bartnik Boundary Data Abstract: The study of static Riemannian metrics arises naturally in general relativity and differential geometry. A static metric produces a special Einstein manifold, and it interconnects with scalar curvature deformation and gluing. The well-known Uniqueness Theorem of Static Black Holes says that an asymptotically flat, static metric with black hole boundary must belong to the Schwarzschild family. In the same vein, most efforts have been made to classify static metrics as known exact solutions. In contrast to the rigidity phenomena and classification efforts, Robert Bartnik proposed the Static Vacuum Extension Conjecture (originating from his other conjectures about quasi-local masses in the 80’s) that there is always a unique, asymptotically flat, static vacuum metric with quite arbitrarily prescribed Bartnik boundary data. In this course, I will discuss some recent progress confirming this conjecture for large classes of boundary data. The course is based on joint work with Zhongshan An, and the tentative plan is 1. The conjecture and an overview of the results
2. Static regular: a sufficient condition for existence and local uniqueness
3. Convex boundary, isometric embedding, and static regular
4. Perturbations of any hypersurface are static regularVideo on Youtube: March 22, 2022
March 29 – April 1, 2022 10:00am – 12:00pm ET, each day Location: Hybrid. CMSA main seminar room, G-10.
Prof. Martin Taylor The nonlinear stability of the Schwarzschild family of black holes Abstract: I will present aspects of a theorem, joint with Mihalis Dafermos, Gustav Holzegel and Igor Rodnianski, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes. April 19 & 21, 2022
10 am – 12 pm ET, each dayZoom onlyProf. Håkan Andréasson Two topics for the Einstein-Vlasov system: Gravitational collapse and properties of static and stationary solutions. Abstract: In these lectures I will discuss the Einstein-Vlasov system in the asymptotically flat case. I will focus on two topics; gravitational collapse and properties of static and stationary solutions. In the former case I will present results in the spherically symmetric case that give criteria on initial data which guarantee the formation of black holes in the evolution. I will also discuss the relation between gravitational collapse for the Einstein-Vlasov system and the Einstein-dust system. I will then discuss properties of static and stationary solutions in the spherically symmetric case and the axisymmetric case. In particular I will present a recent result on the existence of massless steady states surrounding a Schwarzschild black hole. May 16 – 17, 2022
10:00 am – 1:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.Prof. Marcelo Disconzi A brief overview of recent developments in relativistic fluids Abstract: In this series of lectures, we will discuss some recent developments in the field of relativistic fluids, considering both the motion of relativistic fluids in a fixed background or coupled to Einstein’s equations. The topics to be discussed will include: the relativistic free-boundary Euler equations with a physical vacuum boundary, a new formulation of the relativistic Euler equations tailored to applications to shock formation, and formulations of relativistic fluids with viscosity. 1. Set-up, review of standard results, physical motivation.
2. The relativistic Euler equations: null structures and the problem of shocks.
3. The free-boundary relativistic Euler equations with a physical vacuum boundary.
4. Relativistic viscous fluids.
Math Science Lectures in Honor of Raoul Bott: Michael Freedman
On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.This will be the third annual lecture series held in honor of Raoul Bott.
Lecture 1
October 4th, 11:00am (Boston time)Title: The Universe from a single Particle Abstract: I will explore a toy model for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.
Lecture 2
October 5th, 11:00am (Boston time)Title: Controlled Mather Thurston Theorems. Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374
- 2203/22/2022
Flip processes
Abstract: We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself ($k$ is fixed). The process starts with a given $n$-vertex graph $G_0$. In each step, the graph $G_i$ is obtained by sampling $k$ random vertices $v_1,\ldots,v_k$ of $G_{i-1}$ and replacing the induced graph $F:=G_{i-1}[v_1,\ldots,v_k]$ by $\mathcal{R}(F)$. This class contains several previously studied processes including the Erd\H{o}s–R\’enyi random graph process and the triangle removal process.
Given a flip process with a rule $\mathcal{R}$, we construct time-indexed trajectories $\Phi:\Gra\times [0,\infty)\rightarrow\Gra$ in the space of graphons. We prove that for any $T > 0$ starting with a large finite graph $G_0$ which is close to a graphon $W_0$ in the cut norm, with high probability the flip process will stay in a thin sausage around the trajectory $(\Phi(W_0,t))_{t=0}^T$ (after rescaling the time by the square of the order of the graph).
These graphon trajectories are then studied from the perspective of dynamical systems. Among others, we study continuity properties of these trajectories with respect to time and the initial graphon, existence and stability of fixed points and speed of convergence (whenever the infinite time limit exists). We give an example of a flip process with a periodic trajectory. This is joint work with Frederik Garbe, Matas \v Sileikis and Fiona Skerman (arXiv:2201.12272).
We also study several specific families flip processes. This is joint work with Pedro Ara\’ujo, Eng Keat Hng and Matas \v{S}ileikis (in preparation).
A brief introduction to the necessary bits of the theory of graph limits will be given in the talk.Math Science Lectures in Honor of Raoul Bott: Michael Freedman
On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.This will be the third annual lecture series held in honor of Raoul Bott.
Lecture 1
October 4th, 11:00am (Boston time)Title: The Universe from a single Particle Abstract: I will explore a toy model for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.
Lecture 2
October 5th, 11:00am (Boston time)Title: Controlled Mather Thurston Theorems. Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374
- 2203/22/2022
Swampland Program
Please visit the Swampland Initiative for current events.
The Harvard Swampland Initiative is an immersive program aiming to bring together leading experts with the goal of exploring the boundaries of the quantum gravity landscape. Through workshops, seminars, and collaborative research, participants collectively navigate the Swampland, advancing our comprehension of the fundamental principles of quantum gravity.
During the 2021-2022 academic year, the CMSA hosted a program on the so-called “Swampland.”
The Swampland program aims to determine which low-energy effective field theories are consistent with nonperturbative quantum gravity considerations. Not everything is possible in String Theory, and finding out what is and what is not strongly constrains the low energy physics. These constraints are naturally interesting for particle physics and cosmology, which has led to a great deal of activity in the field in the last few years.
The Swampland is intrinsically interdisciplinary, with ramifications in string compactifications, holography, black hole physics, cosmology, particle physics, and even mathematics.
This program will include an extensive group of visitors and a slate of seminars. Additionally, the CMSA will host a school oriented toward graduate students.
Seminars
Swampland Seminar Series & Group Meetings
Program Visitors
- Pieter Bomans, Princeton, 10/30/21 – 11/02/21
- Irene Valenzuela, Instituto de Física Teórica, 02/14/22 – 02/21/22
- Mariana Grana, CEA/Saclay, 03/21/22 – 03/25/22
- Hector Parra De Freitas, IPHT Saclay, 03/21/22 – 04/01/22
- Timo Weigand, 03/21/22 – 03/28/22
- Gary Shiu, University of Wisconsin-Madison, 04/03/22 – 04/10/22
- Thomas van Riet, Leuven University, 04/03/22 – 04/09/22
- Lars Aalsma, University of Wisconsin-Madison, 04/11/22 – 04/15/22
- Sergio Cecotti, 05/08/22 – 05/21/22
- Tom Rudelius, 05/09/22 – 05/13/22
https://sites.harvard.edu/swampland-initiative/
Flip processes
Abstract: We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself ($k$ is fixed). The process starts with a given $n$-vertex graph $G_0$. In each step, the graph $G_i$ is obtained by sampling $k$ random vertices $v_1,\ldots,v_k$ of $G_{i-1}$ and replacing the induced graph $F:=G_{i-1}[v_1,\ldots,v_k]$ by $\mathcal{R}(F)$. This class contains several previously studied processes including the Erd\H{o}s–R\’enyi random graph process and the triangle removal process.
Given a flip process with a rule $\mathcal{R}$, we construct time-indexed trajectories $\Phi:\Gra\times [0,\infty)\rightarrow\Gra$ in the space of graphons. We prove that for any $T > 0$ starting with a large finite graph $G_0$ which is close to a graphon $W_0$ in the cut norm, with high probability the flip process will stay in a thin sausage around the trajectory $(\Phi(W_0,t))_{t=0}^T$ (after rescaling the time by the square of the order of the graph).
These graphon trajectories are then studied from the perspective of dynamical systems. Among others, we study continuity properties of these trajectories with respect to time and the initial graphon, existence and stability of fixed points and speed of convergence (whenever the infinite time limit exists). We give an example of a flip process with a periodic trajectory. This is joint work with Frederik Garbe, Matas \v Sileikis and Fiona Skerman (arXiv:2201.12272).
We also study several specific families flip processes. This is joint work with Pedro Ara\’ujo, Eng Keat Hng and Matas \v{S}ileikis (in preparation).
A brief introduction to the necessary bits of the theory of graph limits will be given in the talk.General Relativity Program Minicourses
CMSA, 20 Garden Street, Cambridge, MA 02138 USAMinicourses
General Relativity Program Minicourses
During the Spring 2022 semester, the CMSA hosted a program on General Relativity.
This semester-long program included four minicourses running in March, April, and May; a conference April 4–8, 2022; and a workshop from May 2–5, 2022.
Schedule Speaker Title Abstract March 1 – 3, 2022
10:00 am – 12:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.Dr. Stefan Czimek Characteristic Gluing for the Einstein Equations Abstract: This course serves as an introduction to characteristic gluing for the Einstein equations (developed by the lecturer in collaboration with S. Aretakis and I. Rodnianski). First we set up and analyze the characteristic gluing problem along one outgoing null hypersurface. Then we turn to bifurcate characteristic gluing (i.e. gluing along two null hypersurfaces bifurcating from a spacelike 2-sphere) and show how to localize characteristic initial data. Subsequently we turn to applications for spacelike initial data. Specifically, we discuss in detail our alternative proofs of the celebrated Corvino-Schoen gluing to Kerr and the Carlotto-Schoen localization of spacelike initial data (with improved decay). March 22 – 25, 2022
22nd & 23rd, 10:00 am – 11:30am ET
24th & 25th, 11:00 am – 12:30pm ETLocation: Hybrid. CMSA main seminar room, G-10.Prof. Lan-Hsuan Huang Existence of Static Metrics with Prescribed Bartnik Boundary Data Abstract: The study of static Riemannian metrics arises naturally in general relativity and differential geometry. A static metric produces a special Einstein manifold, and it interconnects with scalar curvature deformation and gluing. The well-known Uniqueness Theorem of Static Black Holes says that an asymptotically flat, static metric with black hole boundary must belong to the Schwarzschild family. In the same vein, most efforts have been made to classify static metrics as known exact solutions. In contrast to the rigidity phenomena and classification efforts, Robert Bartnik proposed the Static Vacuum Extension Conjecture (originating from his other conjectures about quasi-local masses in the 80’s) that there is always a unique, asymptotically flat, static vacuum metric with quite arbitrarily prescribed Bartnik boundary data. In this course, I will discuss some recent progress confirming this conjecture for large classes of boundary data. The course is based on joint work with Zhongshan An, and the tentative plan is 1. The conjecture and an overview of the results
2. Static regular: a sufficient condition for existence and local uniqueness
3. Convex boundary, isometric embedding, and static regular
4. Perturbations of any hypersurface are static regularVideo on Youtube: March 22, 2022
March 29 – April 1, 2022 10:00am – 12:00pm ET, each day Location: Hybrid. CMSA main seminar room, G-10.
Prof. Martin Taylor The nonlinear stability of the Schwarzschild family of black holes Abstract: I will present aspects of a theorem, joint with Mihalis Dafermos, Gustav Holzegel and Igor Rodnianski, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes. April 19 & 21, 2022
10 am – 12 pm ET, each dayZoom onlyProf. Håkan Andréasson Two topics for the Einstein-Vlasov system: Gravitational collapse and properties of static and stationary solutions. Abstract: In these lectures I will discuss the Einstein-Vlasov system in the asymptotically flat case. I will focus on two topics; gravitational collapse and properties of static and stationary solutions. In the former case I will present results in the spherically symmetric case that give criteria on initial data which guarantee the formation of black holes in the evolution. I will also discuss the relation between gravitational collapse for the Einstein-Vlasov system and the Einstein-dust system. I will then discuss properties of static and stationary solutions in the spherically symmetric case and the axisymmetric case. In particular I will present a recent result on the existence of massless steady states surrounding a Schwarzschild black hole. May 16 – 17, 2022
10:00 am – 1:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.Prof. Marcelo Disconzi A brief overview of recent developments in relativistic fluids Abstract: In this series of lectures, we will discuss some recent developments in the field of relativistic fluids, considering both the motion of relativistic fluids in a fixed background or coupled to Einstein’s equations. The topics to be discussed will include: the relativistic free-boundary Euler equations with a physical vacuum boundary, a new formulation of the relativistic Euler equations tailored to applications to shock formation, and formulations of relativistic fluids with viscosity. 1. Set-up, review of standard results, physical motivation.
2. The relativistic Euler equations: null structures and the problem of shocks.
3. The free-boundary relativistic Euler equations with a physical vacuum boundary.
4. Relativistic viscous fluids.Math Science Lectures in Honor of Raoul Bott: Michael Freedman
On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.This will be the third annual lecture series held in honor of Raoul Bott.
Lecture 1
October 4th, 11:00am (Boston time)Title: The Universe from a single Particle Abstract: I will explore a toy model for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.
Lecture 2
October 5th, 11:00am (Boston time)Title: Controlled Mather Thurston Theorems. Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374
- 2203/22/2022
Flip processes
Abstract: We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself ($k$ is fixed). The process starts with a given $n$-vertex graph $G_0$. In each step, the graph $G_i$ is obtained by sampling $k$ random vertices $v_1,\ldots,v_k$ of $G_{i-1}$ and replacing the induced graph $F:=G_{i-1}[v_1,\ldots,v_k]$ by $\mathcal{R}(F)$. This class contains several previously studied processes including the Erd\H{o}s–R\’enyi random graph process and the triangle removal process.
Given a flip process with a rule $\mathcal{R}$, we construct time-indexed trajectories $\Phi:\Gra\times [0,\infty)\rightarrow\Gra$ in the space of graphons. We prove that for any $T > 0$ starting with a large finite graph $G_0$ which is close to a graphon $W_0$ in the cut norm, with high probability the flip process will stay in a thin sausage around the trajectory $(\Phi(W_0,t))_{t=0}^T$ (after rescaling the time by the square of the order of the graph).
These graphon trajectories are then studied from the perspective of dynamical systems. Among others, we study continuity properties of these trajectories with respect to time and the initial graphon, existence and stability of fixed points and speed of convergence (whenever the infinite time limit exists). We give an example of a flip process with a periodic trajectory. This is joint work with Frederik Garbe, Matas \v Sileikis and Fiona Skerman (arXiv:2201.12272).
We also study several specific families flip processes. This is joint work with Pedro Ara\’ujo, Eng Keat Hng and Matas \v{S}ileikis (in preparation).
A brief introduction to the necessary bits of the theory of graph limits will be given in the talk.Math Science Lectures in Honor of Raoul Bott: Michael Freedman
On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.This will be the third annual lecture series held in honor of Raoul Bott.
Lecture 1
October 4th, 11:00am (Boston time)Title: The Universe from a single Particle Abstract: I will explore a toy model for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.
Lecture 2
October 5th, 11:00am (Boston time)Title: Controlled Mather Thurston Theorems. Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374
- 2203/22/2022
Swampland Program
Please visit the Swampland Initiative for current events.
The Harvard Swampland Initiative is an immersive program aiming to bring together leading experts with the goal of exploring the boundaries of the quantum gravity landscape. Through workshops, seminars, and collaborative research, participants collectively navigate the Swampland, advancing our comprehension of the fundamental principles of quantum gravity.
During the 2021-2022 academic year, the CMSA hosted a program on the so-called “Swampland.”
The Swampland program aims to determine which low-energy effective field theories are consistent with nonperturbative quantum gravity considerations. Not everything is possible in String Theory, and finding out what is and what is not strongly constrains the low energy physics. These constraints are naturally interesting for particle physics and cosmology, which has led to a great deal of activity in the field in the last few years.
The Swampland is intrinsically interdisciplinary, with ramifications in string compactifications, holography, black hole physics, cosmology, particle physics, and even mathematics.
This program will include an extensive group of visitors and a slate of seminars. Additionally, the CMSA will host a school oriented toward graduate students.
Seminars
Swampland Seminar Series & Group Meetings
Program Visitors
- Pieter Bomans, Princeton, 10/30/21 – 11/02/21
- Irene Valenzuela, Instituto de Física Teórica, 02/14/22 – 02/21/22
- Mariana Grana, CEA/Saclay, 03/21/22 – 03/25/22
- Hector Parra De Freitas, IPHT Saclay, 03/21/22 – 04/01/22
- Timo Weigand, 03/21/22 – 03/28/22
- Gary Shiu, University of Wisconsin-Madison, 04/03/22 – 04/10/22
- Thomas van Riet, Leuven University, 04/03/22 – 04/09/22
- Lars Aalsma, University of Wisconsin-Madison, 04/11/22 – 04/15/22
- Sergio Cecotti, 05/08/22 – 05/21/22
- Tom Rudelius, 05/09/22 – 05/13/22
https://sites.harvard.edu/swampland-initiative/
Flip processes
Abstract: We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself ($k$ is fixed). The process starts with a given $n$-vertex graph $G_0$. In each step, the graph $G_i$ is obtained by sampling $k$ random vertices $v_1,\ldots,v_k$ of $G_{i-1}$ and replacing the induced graph $F:=G_{i-1}[v_1,\ldots,v_k]$ by $\mathcal{R}(F)$. This class contains several previously studied processes including the Erd\H{o}s–R\’enyi random graph process and the triangle removal process.
Given a flip process with a rule $\mathcal{R}$, we construct time-indexed trajectories $\Phi:\Gra\times [0,\infty)\rightarrow\Gra$ in the space of graphons. We prove that for any $T > 0$ starting with a large finite graph $G_0$ which is close to a graphon $W_0$ in the cut norm, with high probability the flip process will stay in a thin sausage around the trajectory $(\Phi(W_0,t))_{t=0}^T$ (after rescaling the time by the square of the order of the graph).
These graphon trajectories are then studied from the perspective of dynamical systems. Among others, we study continuity properties of these trajectories with respect to time and the initial graphon, existence and stability of fixed points and speed of convergence (whenever the infinite time limit exists). We give an example of a flip process with a periodic trajectory. This is joint work with Frederik Garbe, Matas \v Sileikis and Fiona Skerman (arXiv:2201.12272).
We also study several specific families flip processes. This is joint work with Pedro Ara\’ujo, Eng Keat Hng and Matas \v{S}ileikis (in preparation).
A brief introduction to the necessary bits of the theory of graph limits will be given in the talk.General Relativity Program Minicourses
CMSA, 20 Garden Street, Cambridge, MA 02138 USAMinicourses
General Relativity Program Minicourses
During the Spring 2022 semester, the CMSA hosted a program on General Relativity.
This semester-long program included four minicourses running in March, April, and May; a conference April 4–8, 2022; and a workshop from May 2–5, 2022.
Schedule Speaker Title Abstract March 1 – 3, 2022
10:00 am – 12:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.Dr. Stefan Czimek Characteristic Gluing for the Einstein Equations Abstract: This course serves as an introduction to characteristic gluing for the Einstein equations (developed by the lecturer in collaboration with S. Aretakis and I. Rodnianski). First we set up and analyze the characteristic gluing problem along one outgoing null hypersurface. Then we turn to bifurcate characteristic gluing (i.e. gluing along two null hypersurfaces bifurcating from a spacelike 2-sphere) and show how to localize characteristic initial data. Subsequently we turn to applications for spacelike initial data. Specifically, we discuss in detail our alternative proofs of the celebrated Corvino-Schoen gluing to Kerr and the Carlotto-Schoen localization of spacelike initial data (with improved decay). March 22 – 25, 2022
22nd & 23rd, 10:00 am – 11:30am ET
24th & 25th, 11:00 am – 12:30pm ETLocation: Hybrid. CMSA main seminar room, G-10.Prof. Lan-Hsuan Huang Existence of Static Metrics with Prescribed Bartnik Boundary Data Abstract: The study of static Riemannian metrics arises naturally in general relativity and differential geometry. A static metric produces a special Einstein manifold, and it interconnects with scalar curvature deformation and gluing. The well-known Uniqueness Theorem of Static Black Holes says that an asymptotically flat, static metric with black hole boundary must belong to the Schwarzschild family. In the same vein, most efforts have been made to classify static metrics as known exact solutions. In contrast to the rigidity phenomena and classification efforts, Robert Bartnik proposed the Static Vacuum Extension Conjecture (originating from his other conjectures about quasi-local masses in the 80’s) that there is always a unique, asymptotically flat, static vacuum metric with quite arbitrarily prescribed Bartnik boundary data. In this course, I will discuss some recent progress confirming this conjecture for large classes of boundary data. The course is based on joint work with Zhongshan An, and the tentative plan is 1. The conjecture and an overview of the results
2. Static regular: a sufficient condition for existence and local uniqueness
3. Convex boundary, isometric embedding, and static regular
4. Perturbations of any hypersurface are static regularVideo on Youtube: March 22, 2022
March 29 – April 1, 2022 10:00am – 12:00pm ET, each day Location: Hybrid. CMSA main seminar room, G-10.
Prof. Martin Taylor The nonlinear stability of the Schwarzschild family of black holes Abstract: I will present aspects of a theorem, joint with Mihalis Dafermos, Gustav Holzegel and Igor Rodnianski, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes. April 19 & 21, 2022
10 am – 12 pm ET, each dayZoom onlyProf. Håkan Andréasson Two topics for the Einstein-Vlasov system: Gravitational collapse and properties of static and stationary solutions. Abstract: In these lectures I will discuss the Einstein-Vlasov system in the asymptotically flat case. I will focus on two topics; gravitational collapse and properties of static and stationary solutions. In the former case I will present results in the spherically symmetric case that give criteria on initial data which guarantee the formation of black holes in the evolution. I will also discuss the relation between gravitational collapse for the Einstein-Vlasov system and the Einstein-dust system. I will then discuss properties of static and stationary solutions in the spherically symmetric case and the axisymmetric case. In particular I will present a recent result on the existence of massless steady states surrounding a Schwarzschild black hole. May 16 – 17, 2022
10:00 am – 1:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.Prof. Marcelo Disconzi A brief overview of recent developments in relativistic fluids Abstract: In this series of lectures, we will discuss some recent developments in the field of relativistic fluids, considering both the motion of relativistic fluids in a fixed background or coupled to Einstein’s equations. The topics to be discussed will include: the relativistic free-boundary Euler equations with a physical vacuum boundary, a new formulation of the relativistic Euler equations tailored to applications to shock formation, and formulations of relativistic fluids with viscosity. 1. Set-up, review of standard results, physical motivation.
2. The relativistic Euler equations: null structures and the problem of shocks.
3. The free-boundary relativistic Euler equations with a physical vacuum boundary.
4. Relativistic viscous fluids.Math Science Lectures in Honor of Raoul Bott: Michael Freedman
On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.This will be the third annual lecture series held in honor of Raoul Bott.
Lecture 1
October 4th, 11:00am (Boston time)Title: The Universe from a single Particle Abstract: I will explore a toy model for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.
Lecture 2
October 5th, 11:00am (Boston time)Title: Controlled Mather Thurston Theorems. Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374