Title: Morse theory & the moduli space of flat connections
Speaker: Prof. Paul Feehan (Rutgers, New Jersey)
Abstract: We shall discuss a variety of results related to Morse (or Morse-Bott) theory for the Yang-Mills energy function on a G-bundle over a closed Riemann manifold, with a long term goal of trying to better understand the meaning of integration over the quotient space of connections. An old result (1985) in a well-known article by Karen Uhlenbeck, asserts that the distance between a connection A and the moduli space of flat connections on a G-bundle over a closed manifold is bounded by a constant times an integral norm of the curvature, F_A, when F_A is suitably small. We shall explain that this result is contradicted by simple examples when the Yang-Mills energy function is not Morse-Bott along the moduli space of flat connections, such as the moduli space of SU(2) connections over a torus. However, a version of Uhlenbeck’s result can be recovered, provided one replaces the norm of the curvature F_A by a suitable power of that quantity, where the power reflects the structure of singularities in the moduli space of flat connections. The proof of our refinement involves gradient flow and Morse theory for the Yang-Mills energy function on the quotient space of connections and a Lojasiewicz distance inequality for the Yang-Mills energy function. In collaboration with Robert and Leslie Sibner in 1990, Uhlenbeck constructed the first examples of non-minimal critical points of the Yang-Mills energy function on SU(2) bundles over the 4-dimensional sphere. We shall describe an approach to constructing arbitrarily high-energy saddle points of the Yang-Mills energy function on SU(2) bundles with any second Chern class over closed Riemannian 4-dimensional manifolds.
Time: Thursday 16 May 2019, 2.30pm
Location: Lecture Room, 1st Floor, School of Theoretical Physics, DIAS, 10 Burlington Road, Dublin 4
Leave a Comment
Last Updated: 13th May 2019 by George Rogers
Thursday 16th May : STP Seminar – Morse theory & the moduli space of flat connections
Title: Morse theory & the moduli space of flat connections
Speaker: Prof. Paul Feehan (Rutgers, New Jersey)
Abstract: We shall discuss a variety of results related to Morse (or Morse-Bott) theory for the Yang-Mills energy function on a G-bundle over a closed Riemann manifold, with a long term goal of trying to better understand the meaning of integration over the quotient space of connections. An old result (1985) in a well-known article by Karen Uhlenbeck, asserts that the distance between a connection A and the moduli space of flat connections on a G-bundle over a closed manifold is bounded by a constant times an integral norm of the curvature, F_A, when F_A is suitably small. We shall explain that this result is contradicted by simple examples when the Yang-Mills energy function is not Morse-Bott along the moduli space of flat connections, such as the moduli space of SU(2) connections over a torus. However, a version of Uhlenbeck’s result can be recovered, provided one replaces the norm of the curvature F_A by a suitable power of that quantity, where the power reflects the structure of singularities in the moduli space of flat connections. The proof of our refinement involves gradient flow and Morse theory for the Yang-Mills energy function on the quotient space of connections and a Lojasiewicz distance inequality for the Yang-Mills energy function. In collaboration with Robert and Leslie Sibner in 1990, Uhlenbeck constructed the first examples of non-minimal critical points of the Yang-Mills energy function on SU(2) bundles over the 4-dimensional sphere. We shall describe an approach to constructing arbitrarily high-energy saddle points of the Yang-Mills energy function on SU(2) bundles with any second Chern class over closed Riemannian 4-dimensional manifolds.
Time: Thursday 16 May 2019, 2.30pm
Location: Lecture Room, 1st Floor, School of Theoretical Physics, DIAS, 10 Burlington Road, Dublin 4
Category: Regular seminars, School of Theoretical Physics News & Events, Uncategorised
...obituaries of prominent individuals The manuscript has been preserved in the @Library_RIA since 1883. (3/3) @HistFest #DIASdiscovers #connacht #books
The Annals of Connacht is a vellum manuscript that was written in the mid-16th century. The contents were derived from older annals compiled for the O’Conors of the Connacht and contain an annual record of significant events over 320 years, and... (2/3)
Date: 19 October 1944 Paper: The Irish Press Synopsis: DIAS has been publishing books since it's founding. One such early publication is the edited manuscript of the Annals of Connacht (Annála Connacht) which was edited for the first time by Martin Freeman of DIAS. (1/3)
This work was to help towards the preservation of the Irish Language, to maintain it's continuity with the past, and was to become a resource for teachers to check pronunciation #DIASdiscovers #Irish #Irishlanguage #CelticStudies #Gaelic
The researchers used the International Phonetic Alphabet, slightly modified to represent vowels and consonants of living speech. At that time there were concerns over the deterioration of the Irish language due to the "overpowering influence of English"
Date: 02 June 1943 Paper: The Irish Press Synopsis: In 1943, a phonetic investigation led by Brian Ó Cuív, Risteárd B. Breathnach and Tomás de Bhaldraithe of DIAS would begin the first systematic scientific recording of the varied sounds of modern Gaelic speech.
Happy Birthday! twitter.com/thecelticist/s…
The papers were 1) Affine Field Theory: conservation identitites and relation to Weyl and Eddington 2)The Union of the three fundamental fields (Gravitation, Menson, Electromagnetism) Which went on to secure worldwide acclaim. #DIASdiscovers
Date: 01 December 1943 Paper: The Irish Press Headline: Two Papers by Dr. Schroedinger Synopsis: 1943 was a busy year for Schroedinger. Not only did he deliver the "What is Life?" Lectures in @tcddublin in February in November he delivered two papers in the @RIAdawson (1/2)
Available to buy on the DIAS bookshop: books.dias.ie/index.php?main… (5/5) #DIASdiscovers #celtic #studies #twopatricks
"In the lives of St. Patrick, the two saints are invariably fused into one", said Prof. O'Rahilly in his lecture. The lecture was a condensation from O’Rahilly’s book “The two Patricks: a lecture on the history of Christianity in fifth-century Ireland”. (4/5)
He was known by his first name Patricius, which in later times would lead to confusion as he was succeeded by another apostle of the same name (Saint Patrick or Patricius in Latin). (3/5)
He spoke on "Palladius and Patrick". Palladius was the first bishop of the Christians of Ireland. (2/5)
Date: 21st March 1942 Paper: The Irish Press Headline: Palladius and Patrick | School Of Celtic Studies Lecture Synopsis: The first public lecture under the auspices of the School of Celtic Studies was delivered in Trinity College by Professor T. F. O'Rahilly in 1942. (1/5)
As part of our ongoing participation in the @HistFest we decided to take a look into the Irish Newspaper Archives and see where DIAS made it into print over the last 80 years. There were so many articles, the hardest part was selecting what we would post. We hope you enjoy!
@AReillyFailte @CultureNight @VisitDublin Thanks Antoinette! Glad you enjoyed 😊