Thammasat University

"Ola Bratteli"

Mathematical Physics Seminar

and

Mathematics in Thailand Colloquium

"Ola Bratteli"

Mathematical Physics Seminar

and

Mathematics in Thailand Colloquium

Dedicated to the
memory of Ola
Bratteli

Seminar's sessions are informally organized once or twice every month at the Department of Mathematics and Statistics in Thammasat University Rangsit Campus.

The format of the gatherings comprise a one-two hours academic seminar, followed by one-two hours of discussion forum that can be followed by a dinner.

The topics covered by the Mathematical Physics Seminar are mainly (but not exclusively) related to: operator algebras, non-commutative geometry, mathematical physics, quantum theory, differential geometry, category theory, philosophy/history of physics/mathematics and occasionally other general science areas.

The Mathematics in Thailand Colloquium aims to showcase some of the best mathematicians and scientists in Thailand, inviting young active researchers (but occasionally senior academics) that, through direct discussion, can inspire and widen the perspectives of graduate students and faculty members alike.

For information please contact: Paolo Bertozzini

The seminar is partially supported by Thammasat University Research Grant 2/15/2556 "Categorical Non-commutative Geometry".

__Friday
22__
February 2019
- Room LC2-230
- Time:
16.00-18.30
- Mathematics
in Thailand
Colloquium

Peter Haddawy - Mahidol University - Thailand

Title: Spatio-temporal Bayesian Networks for Malaria Prediction [slides]

Abstract: Targeted intervention and resource allocation are essential for effective malaria control, particularly in remote areas, with predictive models providing important information for decision making. While a diversity of modeling technique have been used to create predictive models of malaria, no work has made use of Bayesian networks. Bayes nets are attractive due to their ability to represent uncertainty, model time lagged and nonlinear relations, and provide explanations. In this talk I discuss the use of Bayesian networks to model malaria, demonstrating the approach by creating village level models with weekly temporal resolution for Tha Song Yang district in northern Thailand. The networks are learned using data on cases and environmental covariates. Three types of networks are explored: networks for numeric prediction, networks for outbreak prediction, and networks that incorporate spatial autocorrelation. Evaluation of the numeric prediction network shows that the Bayes net has prediction accuracy in terms of mean absolute error of about 1.4 cases for 1 week prediction and 1.7 cases for 6 week prediction. The network for outbreak prediction has an ROC AUC above 0.9 for all prediction horizons. Comparison of prediction accuracy of both Bayes nets against several traditional modeling approaches shows the Bayes nets to outperform the other models for longer time horizon prediction of high incidence transmission. To model spread of malaria over space, we elaborate the models with links between the village networks. This results in some very large models which would be far too laborious to build by hand. So we represent the models as collections of probability logic rules and automatically generate the networks. Evaluation of the models shows that the autocorrelation links significantly improve prediction accuracy for some villages in regions of high incidence. We conclude that spatiotemporal Bayesian networks are a highly promising modeling alternative for prediction of malaria and other vector-borne diseases.

Monday 04 March 2019 - Room LC2-230 - Time: 15.00-18.30 - Mathematics in Thailand Colloquium

Przemo Kranz - University of Mississippi - USA (retired)

Title: Great Solved Problems [slides - to be uploaded]

Abstract: Having been involved in mathematical research for 50 years I have witnessed an impressive development of mathematical ideas over that period. Many outstanding problems from the past, some of which intrigued mathematicians for generations, have been solved. I will discuss a selection of these problems such as

(0) Axiom of Choice, (1) Continuum Hypothesis, (2) Basis Problem, Approximation Problem (3) Apèry Theorem, (4) Four Color Problem, (5) Bieberbach Conjecture, (6) Mordell Conjecture, (7) Invariant Subspace Problem, (8) Fermat Great Theorem, (9) Unconditional Basic Sequence, (10) Maharam Problem, (11) Poincaré Hypothesis, (12) Primes in Arithmetic Progression ; and two partially solved important old problems (a) Twin Primes Conjecture, (b) Goldbach Hypothesis.

There were, of course, many other important problems that were successfully solved in the recent past. And there were still many more important problems that emerged over that period, quite often in the areas of mathematics that did not even exist 50 years ago. The relentless progress or mathematical ideas is one of the most captivating stories of our civilization.

Monday 18 March - Room LC2-230 - Time: 15.00-18.30 - Mathematical Physics Seminar

Tony C. Scott - Taiyuan University of Technology Shanxi - China (retired)

Title: Molecular Physics, Gravity and the Lambert W Function [slides - to be uploaded]

Abstract: The impetus arose from the fact that complete analytical solutions for the metric of a covariant N-body system has proven elusive in General Relativity. To simplify the problem, the number of dimensions was lowered to 1+1 namely one spatial dimension and one time dimension. This model known as R=T theory (as opposed to the general G=T theory) involves a gravitational dilaton - which has speculated connections to the Higgs boson - and is to amenable amenable to exact solutions. Moreover its field equation is none other that the Schroedinger equation. This work has been recently generalized back to our world, namely 3+1 dimensions, where again the field equation for the dilaton is a logarithmic Schroedinger equation which is seen in Bose-Einstein condensates and Superfluid Vacuum Theory (SVT). Thus one obtains a normalizable theory combining gravity, quantization and even electromagnetic interactions.

__Tuesday__
26 - __Wednesday__
27 March -
Room LC2-230 -
Time: __13.30-16.30__
- Mathematical
Physics __Workshop
__

Gaywalee Yamskulna - Illinois State University - Normal - USA

Title: Vertex Algebras [slides - to be uploaded]

Abstract: Vertex algebra was introduced to mathematics in the work of Borcherds and Frenkel, Lepowsky and Meurman in 1980’s. In physics they appeared in the string theory literature as chiral algebras of two-dimensional conformal field theory. Since their introduction, vertex algebras have proven to be a truly universal algebraic structure which have found connections and applications in many fields in mathematics and physics.

In this lecture series, I will introduce vertex algebras and discuss about their general properties. Also, I will provide many interesting examples of vertex (operator) algebras. Finally, I will discuss about N-graded vertex (operator) algebras.

List of Topics:

(1) Vertex algebras,

(2) Locality and quantum fields,

(3) Conformal Field Theory axioms,

(4) Lie algebras and local fields,

(5) Vertex operator algebras,

(6) Modules over a vertex operator algebra,

(7) Structure of N-graded vertex operator algebras,

(8) Shifted theory of vertex operator algebras,

(9) Vertex algebras and their modules associated with vertex algebroids.

To Be Announced - Room LC2-230 - Time: 15.00-18.30 - Mathematical Physics Seminar

Tirasan Khandhawit - Okinawa Institute of Science and Technology - Japan

Title: A Brief History of Low-dimensional Topology [slides - to be uploaded]

Abstract: I will give an overview of the study of low-dimensional topology in the past.

An object of interest is called a manifold, which generalizes a concept of curve and surface.

I will try to convince how dimension 3 and 4 are special.

Title: Stable Homotopy Refinement of Seiberg-Witten theory [slides - to be uploaded]

Abstract: Seiberg-Witten theory has become a very useful tool in the study of 3,4-manifolds in the past decades.

I will try to describe my main research interest which focus on stable homotopy refinement of this theory.

To Be Rescheduled - Room LC2-230 - Time: 15.00-18.30 - Mathematics in Thailand Colloquium

David Yost - Federation University - Ballarat - Australia

Title: To Be Announced [slides - to be uploaded]

Abstract: To Be Announced

To Be Rescheduled - Room LC2-230 - Time: 15.00-18.30 - Mathematics in Thailand Colloquium

Anna Kamińska - University of Memphis - USA

Title: Geometric Properties of Noncommutative Symmetric Spaces of Measurable Operators and Unitary Matrix Ideals [slides - to be uploaded]

Abstract: This is a survey lecture presenting a number of geometric properties of non-commutative symmetric spaces of measurable operators E(M, τ) and unitary matrix ideals C_{E},
where M is a von Neumann algebra with a semi-finite,
faithful and normal trace τ, and E is a (quasi)
Banach function space and a sequence lattice,
respectively. We provide auxiliary definitions,
notions, examples and we discuss a number of
properties that are most often used in studies of
local and global geometry of (quasi) Banach spaces.
We interpret the general spaces E(M, τ) in the case
when E=L_{p} obtaining L_{p}(M, τ)
spaces, and in the case when E is a sequence space
we explain how the unitary matrix space C_{E}
can be in fact identified with the symmetric space
of measurable operators G(M, τ) for some Banach
function lattice G. We present the results on
(complex) extreme points, (complex) strict
convexity, strong extreme points and midpoint local
uniform convexity, k-extreme points and k-convexity,
(complex or local) uniform convexity, smoothness and
strong smoothness, (strongly) exposed points,
(uniform) Kadec-Klee properties, Banach-Saks
properties, Radon-Nikodym property and stability in
the sense of Krivine-Maurey. We also present some
open problems.

Seminar's sessions are informally organized once or twice every month at the Department of Mathematics and Statistics in Thammasat University Rangsit Campus.

The format of the gatherings comprise a one-two hours academic seminar, followed by one-two hours of discussion forum that can be followed by a dinner.

The topics covered by the Mathematical Physics Seminar are mainly (but not exclusively) related to: operator algebras, non-commutative geometry, mathematical physics, quantum theory, differential geometry, category theory, philosophy/history of physics/mathematics and occasionally other general science areas.

The Mathematics in Thailand Colloquium aims to showcase some of the best mathematicians and scientists in Thailand, inviting young active researchers (but occasionally senior academics) that, through direct discussion, can inspire and widen the perspectives of graduate students and faculty members alike.

For information please contact: Paolo Bertozzini

The seminar is partially supported by Thammasat University Research Grant 2/15/2556 "Categorical Non-commutative Geometry".

Forthcoming Meetings

Peter Haddawy - Mahidol University - Thailand

Title: Spatio-temporal Bayesian Networks for Malaria Prediction [slides]

Abstract: Targeted intervention and resource allocation are essential for effective malaria control, particularly in remote areas, with predictive models providing important information for decision making. While a diversity of modeling technique have been used to create predictive models of malaria, no work has made use of Bayesian networks. Bayes nets are attractive due to their ability to represent uncertainty, model time lagged and nonlinear relations, and provide explanations. In this talk I discuss the use of Bayesian networks to model malaria, demonstrating the approach by creating village level models with weekly temporal resolution for Tha Song Yang district in northern Thailand. The networks are learned using data on cases and environmental covariates. Three types of networks are explored: networks for numeric prediction, networks for outbreak prediction, and networks that incorporate spatial autocorrelation. Evaluation of the numeric prediction network shows that the Bayes net has prediction accuracy in terms of mean absolute error of about 1.4 cases for 1 week prediction and 1.7 cases for 6 week prediction. The network for outbreak prediction has an ROC AUC above 0.9 for all prediction horizons. Comparison of prediction accuracy of both Bayes nets against several traditional modeling approaches shows the Bayes nets to outperform the other models for longer time horizon prediction of high incidence transmission. To model spread of malaria over space, we elaborate the models with links between the village networks. This results in some very large models which would be far too laborious to build by hand. So we represent the models as collections of probability logic rules and automatically generate the networks. Evaluation of the models shows that the autocorrelation links significantly improve prediction accuracy for some villages in regions of high incidence. We conclude that spatiotemporal Bayesian networks are a highly promising modeling alternative for prediction of malaria and other vector-borne diseases.

Monday 04 March 2019 - Room LC2-230 - Time: 15.00-18.30 - Mathematics in Thailand Colloquium

Przemo Kranz - University of Mississippi - USA (retired)

Title: Great Solved Problems [slides - to be uploaded]

Abstract: Having been involved in mathematical research for 50 years I have witnessed an impressive development of mathematical ideas over that period. Many outstanding problems from the past, some of which intrigued mathematicians for generations, have been solved. I will discuss a selection of these problems such as

(0) Axiom of Choice, (1) Continuum Hypothesis, (2) Basis Problem, Approximation Problem (3) Apèry Theorem, (4) Four Color Problem, (5) Bieberbach Conjecture, (6) Mordell Conjecture, (7) Invariant Subspace Problem, (8) Fermat Great Theorem, (9) Unconditional Basic Sequence, (10) Maharam Problem, (11) Poincaré Hypothesis, (12) Primes in Arithmetic Progression ; and two partially solved important old problems (a) Twin Primes Conjecture, (b) Goldbach Hypothesis.

There were, of course, many other important problems that were successfully solved in the recent past. And there were still many more important problems that emerged over that period, quite often in the areas of mathematics that did not even exist 50 years ago. The relentless progress or mathematical ideas is one of the most captivating stories of our civilization.

Monday 18 March - Room LC2-230 - Time: 15.00-18.30 - Mathematical Physics Seminar

Tony C. Scott - Taiyuan University of Technology Shanxi - China (retired)

Title: Molecular Physics, Gravity and the Lambert W Function [slides - to be uploaded]

Abstract: The impetus arose from the fact that complete analytical solutions for the metric of a covariant N-body system has proven elusive in General Relativity. To simplify the problem, the number of dimensions was lowered to 1+1 namely one spatial dimension and one time dimension. This model known as R=T theory (as opposed to the general G=T theory) involves a gravitational dilaton - which has speculated connections to the Higgs boson - and is to amenable amenable to exact solutions. Moreover its field equation is none other that the Schroedinger equation. This work has been recently generalized back to our world, namely 3+1 dimensions, where again the field equation for the dilaton is a logarithmic Schroedinger equation which is seen in Bose-Einstein condensates and Superfluid Vacuum Theory (SVT). Thus one obtains a normalizable theory combining gravity, quantization and even electromagnetic interactions.

Gaywalee Yamskulna - Illinois State University - Normal - USA

Title: Vertex Algebras [slides - to be uploaded]

Abstract: Vertex algebra was introduced to mathematics in the work of Borcherds and Frenkel, Lepowsky and Meurman in 1980’s. In physics they appeared in the string theory literature as chiral algebras of two-dimensional conformal field theory. Since their introduction, vertex algebras have proven to be a truly universal algebraic structure which have found connections and applications in many fields in mathematics and physics.

In this lecture series, I will introduce vertex algebras and discuss about their general properties. Also, I will provide many interesting examples of vertex (operator) algebras. Finally, I will discuss about N-graded vertex (operator) algebras.

List of Topics:

(1) Vertex algebras,

(2) Locality and quantum fields,

(3) Conformal Field Theory axioms,

(4) Lie algebras and local fields,

(5) Vertex operator algebras,

(6) Modules over a vertex operator algebra,

(7) Structure of N-graded vertex operator algebras,

(8) Shifted theory of vertex operator algebras,

(9) Vertex algebras and their modules associated with vertex algebroids.

To Be Announced - Room LC2-230 - Time: 15.00-18.30 - Mathematical Physics Seminar

Tirasan Khandhawit - Okinawa Institute of Science and Technology - Japan

Title: A Brief History of Low-dimensional Topology [slides - to be uploaded]

Abstract: I will give an overview of the study of low-dimensional topology in the past.

An object of interest is called a manifold, which generalizes a concept of curve and surface.

I will try to convince how dimension 3 and 4 are special.

Title: Stable Homotopy Refinement of Seiberg-Witten theory [slides - to be uploaded]

Abstract: Seiberg-Witten theory has become a very useful tool in the study of 3,4-manifolds in the past decades.

I will try to describe my main research interest which focus on stable homotopy refinement of this theory.

To Be Rescheduled - Room LC2-230 - Time: 15.00-18.30 - Mathematics in Thailand Colloquium

David Yost - Federation University - Ballarat - Australia

Title: To Be Announced [slides - to be uploaded]

Abstract: To Be Announced

To Be Rescheduled - Room LC2-230 - Time: 15.00-18.30 - Mathematics in Thailand Colloquium

Anna Kamińska - University of Memphis - USA

Title: Geometric Properties of Noncommutative Symmetric Spaces of Measurable Operators and Unitary Matrix Ideals [slides - to be uploaded]

Abstract: This is a survey lecture presenting a number of geometric properties of non-commutative symmetric spaces of measurable operators E(M, τ) and unitary matrix ideals C

Previous
Meetings

__Tuesday
04__
December 2018
- Room LC2-230
- Time:
15.00-18.30
- Mathematics
in Thailand
Colloquium

Robert Egrot - Mahidol University - Thailand

Title: Canonicity in Algebra and Logic [slides]

Abstract: This talk is intended to be an introductory survey of the broad area of algebraic logic, a subject sitting neatly in the intersection of classical mathematics, computer science and philosophy. This survey will necessarily be light on both technical details and coverage, but I hope to convey at least a sense of the big ideas involved. The focus will be the algebraic/order theoretic notion of a canonical extension, its history, and its role in the theory of non-classical logics. The aim of the talk is to build up to a rough understanding of the sentence "canonical extensions provide completeness results for substructural logics with respect to relational semantics".

__Friday
30 __November
2018 - Room
LC2-230 -
Time:
15.00-18.30
- Mathematical
Physics
Seminar

Watthanan Jatuviriyapornchai - Mahidol University - Thailand

Title: Derivation of Mean-field Equations for Stochastic Particle Systems [slides]

Abstract: We study the single site dynamics in stochastic particle systems of misanthrope type with bounded rates on a complete graph. In the limit of diverging system size we establish convergence to a Markovian non-linear birth death chain, described by a mean-field equation known also from exchange-driven growth processes. Conservation of mass in the particle system leads to conservation of the first moment for the limit dynamics, and to non-uniqueness of stationary measures. The proof is based on a coupling to branching processes via the graphical construction, and establishing uniqueness of the solution for the limit dynamics. As particularly interesting examples we discuss the dynamics of two models that exhibit a condensation transition and their connection to exchange-driven growth processes.

__Tuesday
27__ November
- Room LC2-230
- Time: **15.00-16.30**
- Mathematics
in Thailand
Colloquium

Chee Yap - Courant Institute - New York University - USA

Title: Isolating Simple Roots of Zero-Dimensional Real Systems [slides]

Abstract: We describe a new algorithm for isolating simple real roots of a zero-dimensional system of equations within a box region. The equations need not be polynomial. Our subdivision-based algorithm is effective in that it provides explicit precision requirements to justify a rigorous implementation. This is aided by the use of 3 levels of abstraction of our algorithmic primitives.

The main predicate is the Moore-Kostelides (MK) test, based on the Miranda Theorem (1940). Although the MK test is well-known in interval community, to our knowledge, it has not been synthesized into a complete global algorithm. Our algorithm uses two other predicates: an exclusion and a Jacobian test.

We provide a complexity analysis of our algorithm based on intrinsic geometric parameters.

(Joint Work with Juan Xu).

__Friday
16__ November
- Room LC2-230
- Time: **09.00-12.00**
- Mathematics
in Thailand
Colloquium

Pichet Chaoha - Chulalongkorn University - Thailand

Title: Virtual Stability and Fixed Point Sets [slides]

Abstract: Virtual stability is a useful concept in relating the fixed point set of a selfmap on a Hausdorff space to its convergence set. In this talk, we will present the motivation and the development of virtual stability. Recent results and some applications will be also discussed.

__Friday
09__
November 2018
- Room LC2-230
- Time:
15.00-18.30
- Mathematics
in Thailand
Colloquium

Prof. Dmitry Feichtner-Kozlov - University of Bremen - Germany

Title: An Invitation to Applied Topology [slides]

Abstract: Applied Topology is a modern and dynamic research field in Mathematics, which combines theoretical rigour, combinatorial complexity, and focus on applications both in other fields in mathematics, as well as in other sciences. In this talk we give a gentle introduction to the topic by focusing our attention on two aspects: connections between Discrete Mathematics and Applied Topology, and applications to the Theoretical Computer Science, specifically to Distributed Computing.

Wayne Lawton - Siberian Federal University - Krasnoyarks - Russia

Title: Fourier Representation of Polynomial Ideals [slides]

Abstract: Given a polynomial ideal I in n variables we let R(I) denote the vector space of functions f on the rank n lattice such that PF = 0 for all P in I. Here F denotes the formal power series with coefficients f. We prove that a function f is in R(I) iff it equals the complex Fourier transform of a distribution D supported on the variety V(I) and Pf = 0. This characterized the multiplicity variety associated with I. Our proof develops a new fibered method to lift analytic functionals and our result extends those of Ehrenpreis, Hormander, Malgrange and Palmadorov that represent solutions of certain partial differential equations by complex Fourier transforms. We suggest potential extensions to ideals in Weyl algebras.

4-15 August 2018 - "Ola Bratteli" Workshop on Operator Algebras

Robert Egrot - Mahidol University - Thailand

Title: Canonicity in Algebra and Logic [slides]

Abstract: This talk is intended to be an introductory survey of the broad area of algebraic logic, a subject sitting neatly in the intersection of classical mathematics, computer science and philosophy. This survey will necessarily be light on both technical details and coverage, but I hope to convey at least a sense of the big ideas involved. The focus will be the algebraic/order theoretic notion of a canonical extension, its history, and its role in the theory of non-classical logics. The aim of the talk is to build up to a rough understanding of the sentence "canonical extensions provide completeness results for substructural logics with respect to relational semantics".

Watthanan Jatuviriyapornchai - Mahidol University - Thailand

Title: Derivation of Mean-field Equations for Stochastic Particle Systems [slides]

Abstract: We study the single site dynamics in stochastic particle systems of misanthrope type with bounded rates on a complete graph. In the limit of diverging system size we establish convergence to a Markovian non-linear birth death chain, described by a mean-field equation known also from exchange-driven growth processes. Conservation of mass in the particle system leads to conservation of the first moment for the limit dynamics, and to non-uniqueness of stationary measures. The proof is based on a coupling to branching processes via the graphical construction, and establishing uniqueness of the solution for the limit dynamics. As particularly interesting examples we discuss the dynamics of two models that exhibit a condensation transition and their connection to exchange-driven growth processes.

Chee Yap - Courant Institute - New York University - USA

Title: Isolating Simple Roots of Zero-Dimensional Real Systems [slides]

Abstract: We describe a new algorithm for isolating simple real roots of a zero-dimensional system of equations within a box region. The equations need not be polynomial. Our subdivision-based algorithm is effective in that it provides explicit precision requirements to justify a rigorous implementation. This is aided by the use of 3 levels of abstraction of our algorithmic primitives.

The main predicate is the Moore-Kostelides (MK) test, based on the Miranda Theorem (1940). Although the MK test is well-known in interval community, to our knowledge, it has not been synthesized into a complete global algorithm. Our algorithm uses two other predicates: an exclusion and a Jacobian test.

We provide a complexity analysis of our algorithm based on intrinsic geometric parameters.

(Joint Work with Juan Xu).

Pichet Chaoha - Chulalongkorn University - Thailand

Title: Virtual Stability and Fixed Point Sets [slides]

Abstract: Virtual stability is a useful concept in relating the fixed point set of a selfmap on a Hausdorff space to its convergence set. In this talk, we will present the motivation and the development of virtual stability. Recent results and some applications will be also discussed.

Prof. Dmitry Feichtner-Kozlov - University of Bremen - Germany

Title: An Invitation to Applied Topology [slides]

Abstract: Applied Topology is a modern and dynamic research field in Mathematics, which combines theoretical rigour, combinatorial complexity, and focus on applications both in other fields in mathematics, as well as in other sciences. In this talk we give a gentle introduction to the topic by focusing our attention on two aspects: connections between Discrete Mathematics and Applied Topology, and applications to the Theoretical Computer Science, specifically to Distributed Computing.

Monday
22 October
2018 - Room
LC2-230 -
Time:
15.00-18.30
- Mathematics
in Thailand
Colloquium

Keng Wiboontan - Chulalongkorn University - Thailand

Title: Linear Representations of a Gyrogroup and Möbius's Functional Equation [slides]

Abstract: In this talk, at the beginning I will give an introduction to the gyrogroup structure first proposed by Abraham A.Ungar in 1988. At first, the gyrogroup structure was used to describe an algebraic structure hidden inside Einstein's velocity addition in special relativity. A gyrogroup encodes a group-like structure but it lacks the usual associative law. In stead, any gyrogroup has the so-called gyroassociative law. This law reflects the intricate structure in Einstein's velocity addition. The two main examples of gyrogroups are the Einstein gyrogroup and the Möbius gyrogroup. Many algebraic properties of gyrogroups have bee studied extensively. Recently, Teerapong Suksumran gave a definition of gyrogroup actions. I will present a joint work with him where we define linear representations of a gyrogroup and then obtain some analogous results as those of representations of a group. Then to find concrete examples of irreducible representations of the Möbius gyrogroup, one need to solve the so-called Möbius's functional equation.

Monday 08 October 2018 - Room LC2-230 - Time: 15.00-18.30 - Mathematical Physics Seminar

Sujin Suwanna - Mahidol University (Optical and Quantum Physics Laboratory, Department of Physics) - Thailand

Title: Dynamics of Open Quantum Systems and Decoherence Feedback Control [slides - to be uploaded]

Abstract: In closed quantum systems, dynamics of quantum states are described by one-parameter strongly continuous unitary groups, where the Hamiltonian corresponding to the Schrödinger or the Liouville-von Neumann equation is a generator of the unitary groups, acting on a Hilbert space of square-integrable functions. In open quantum systems, where interaction with environment is essential, so decoherence is induced, the dynamics are described instead by semigroups. Several types of dynamical maps are possible depending on the nature of the environment and the interaction. In this talk, we will discuss the Lindblad dynamical maps and the Markovian environment. We will show that under some reasonable physically-motivated assumptions, the dynamical map can be decomposed into a unitary component corresponding to a reversible process, and a semigroup corresponding to an irreversible process, hence the entropy change. When the environment is assumed to be Markovian, the Ito's and Stratonovich's stochastic master equations can be derived. If an open quantum system sacrifices part of its subsystem to probe the environmental response, a feedback control is possible to cancel the decoherence. This gives rise to potential of fidelity control in open quantum systems for purposes of quantum computing and information processing. Keywords: dynamical maps, open quantum systems, stochastic master equation, decoherence.

Monday 10 September 2018 - Room LC2-230 - Time: 15.00-18.30 - Mathematical Physics Seminar

Mairi Sakellariadou - King's College - London - UK

Title: Aspects of the Bosonic Spectral Action for Almost Commutative Manifolds [slides - to be uploaded]

Abstract: I will review the noncommutative spectral geometry, a gravitational model that combines noncommutative geometry with the spectral action principle, in an attempt to unify General Relativity and the Standard Model of electroweak and strong interactions. I will briefly present phenomenological consequences, address some open questions and discuss the gravitational sector of the theory.

Mairi Sakellariadou - King's College - London - UK

Title: Noncommutative Gravity with Self-dual Variables [slides - to be uploaded]

Abstract: I will present a noncommutative extension of Palatini-Holst theory on a twist-deformed spacetime. The twist deformation entails an enlargement of the gauge group, and leads to the introduction of new gravitational degrees of freedom. In particular, the tetrad degrees of freedom must be doubled, thus leading to a bitetrad theory of gravity. I will study the commutative limit of the model, focusing in particular on the role of torsion and non-metricity. I will briefly comment on connections with bimetric theories and the role of local conformal invariance in the commutative limit.

Monday
20 August -
Room LC2-230 -
Time:
15.00-18.30
- Mathematics
in Thailand
ColloquiumKeng Wiboontan - Chulalongkorn University - Thailand

Title: Linear Representations of a Gyrogroup and Möbius's Functional Equation [slides]

Abstract: In this talk, at the beginning I will give an introduction to the gyrogroup structure first proposed by Abraham A.Ungar in 1988. At first, the gyrogroup structure was used to describe an algebraic structure hidden inside Einstein's velocity addition in special relativity. A gyrogroup encodes a group-like structure but it lacks the usual associative law. In stead, any gyrogroup has the so-called gyroassociative law. This law reflects the intricate structure in Einstein's velocity addition. The two main examples of gyrogroups are the Einstein gyrogroup and the Möbius gyrogroup. Many algebraic properties of gyrogroups have bee studied extensively. Recently, Teerapong Suksumran gave a definition of gyrogroup actions. I will present a joint work with him where we define linear representations of a gyrogroup and then obtain some analogous results as those of representations of a group. Then to find concrete examples of irreducible representations of the Möbius gyrogroup, one need to solve the so-called Möbius's functional equation.

Monday 08 October 2018 - Room LC2-230 - Time: 15.00-18.30 - Mathematical Physics Seminar

Sujin Suwanna - Mahidol University (Optical and Quantum Physics Laboratory, Department of Physics) - Thailand

Title: Dynamics of Open Quantum Systems and Decoherence Feedback Control [slides - to be uploaded]

Abstract: In closed quantum systems, dynamics of quantum states are described by one-parameter strongly continuous unitary groups, where the Hamiltonian corresponding to the Schrödinger or the Liouville-von Neumann equation is a generator of the unitary groups, acting on a Hilbert space of square-integrable functions. In open quantum systems, where interaction with environment is essential, so decoherence is induced, the dynamics are described instead by semigroups. Several types of dynamical maps are possible depending on the nature of the environment and the interaction. In this talk, we will discuss the Lindblad dynamical maps and the Markovian environment. We will show that under some reasonable physically-motivated assumptions, the dynamical map can be decomposed into a unitary component corresponding to a reversible process, and a semigroup corresponding to an irreversible process, hence the entropy change. When the environment is assumed to be Markovian, the Ito's and Stratonovich's stochastic master equations can be derived. If an open quantum system sacrifices part of its subsystem to probe the environmental response, a feedback control is possible to cancel the decoherence. This gives rise to potential of fidelity control in open quantum systems for purposes of quantum computing and information processing. Keywords: dynamical maps, open quantum systems, stochastic master equation, decoherence.

Monday 10 September 2018 - Room LC2-230 - Time: 15.00-18.30 - Mathematical Physics Seminar

Mairi Sakellariadou - King's College - London - UK

Title: Aspects of the Bosonic Spectral Action for Almost Commutative Manifolds [slides - to be uploaded]

Abstract: I will review the noncommutative spectral geometry, a gravitational model that combines noncommutative geometry with the spectral action principle, in an attempt to unify General Relativity and the Standard Model of electroweak and strong interactions. I will briefly present phenomenological consequences, address some open questions and discuss the gravitational sector of the theory.

Mairi Sakellariadou - King's College - London - UK

Title: Noncommutative Gravity with Self-dual Variables [slides - to be uploaded]

Abstract: I will present a noncommutative extension of Palatini-Holst theory on a twist-deformed spacetime. The twist deformation entails an enlargement of the gauge group, and leads to the introduction of new gravitational degrees of freedom. In particular, the tetrad degrees of freedom must be doubled, thus leading to a bitetrad theory of gravity. I will study the commutative limit of the model, focusing in particular on the role of torsion and non-metricity. I will briefly comment on connections with bimetric theories and the role of local conformal invariance in the commutative limit.

Wayne Lawton - Siberian Federal University - Krasnoyarks - Russia

Title: Fourier Representation of Polynomial Ideals [slides]

Abstract: Given a polynomial ideal I in n variables we let R(I) denote the vector space of functions f on the rank n lattice such that PF = 0 for all P in I. Here F denotes the formal power series with coefficients f. We prove that a function f is in R(I) iff it equals the complex Fourier transform of a distribution D supported on the variety V(I) and Pf = 0. This characterized the multiplicity variety associated with I. Our proof develops a new fibered method to lift analytic functionals and our result extends those of Ehrenpreis, Hormander, Malgrange and Palmadorov that represent solutions of certain partial differential equations by complex Fourier transforms. We suggest potential extensions to ideals in Weyl algebras.

4-15 August 2018 - "Ola Bratteli" Workshop on Operator Algebras