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
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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
You're invited to join us for the @StpDias Statutory Public Lecture 2019 on 23 May 2019, 6pm by Prof. Don Zagier in @tcddublin. Prof. Zaigier will deliver an exciting look at 'Numbers, Knots, & Quantum Theory'. Info and tickets at: bit.ly/2JLsAUj #DIASdiscovers
As part of IQF 2019 on 22 May, Prof. Marika Taylor will explain what #BlackHoles might teach us about #QuantumComputing and conversely, what quantum theory implies about the fundamental properties of black holes. Register at bit.ly/2WuKgHo #DIASdiscovers
The annual Irish Quantum Foundations meeting will take place this year in @tcddublin on 23 & 24 May, bringing together Irish and international theoretical physicists who work fundamental theory and quantum foundations. More info and registration at maths.tcd.ie/~tristan/IQF20….
At last week's final #WhatIsLife lecture, Director of @StpDias Professor Werner Nahm contemplated the impact of Ada Yonath's work for the question 'what is life?' and tying into the impact and legacy of #Schrödinger. #DIASdiscovers
Martin Möllhoff, Director of Irish National Seismic Network spoke to @OceanFmIreland about yesterday's earthquake in Donegal. You can lsiten back at: oceanfm.ie/2019/04/30/ano… #DIASdiscovers
On Thursday, Werner Nahm had us 'thinking outside the box' at the fourth and final @DIAS_Dublin 'What is Life?' lecture series. The series commemorated the 75th anniversary of Erwin #Schrödinger's ground breaking series being published as a book. #DIASdiscovers
Another Earthquake recorded in Donegal by the Irish National Seismic Network. Magnitude 2.1. You can read more about it at tinyurl.com/y4bewx3h. #DIASdiscovers twitter.com/dias_geophysic…
If you haven't booked your place at today's lunchtime lecture from the @StpDias, exploring the legacy of Schrödinger’s 'What is Life?' lectures and book, do so now at: bit.ly/2KZStSH It's te final one lecture of the series. #DIASdiscovers
Don't miss the 4th and final lecture in our #WhatisLife series with Prof Werner Nahm, Director of @StpDias, looking at ‘Beyond the ‘What is Life?’ lectures and book’. This lecture, at 1pm tomorrow, will explore the legacy of Professor Erwin Schrödinger. bit.ly/2KZStSH
#DidYouKnow the recent earthquake in Donegal was not the county's first? In fact, they're well used to a tremor or 2.7 in the North West. Read about the county's ground shaking history in The @IrishTimes at: bit.ly/2UTkAHw #DIASdiscovers
#OTD John T. Lewis was born in 1932. Lewis served as Director of @StpDias and was described by @IrishTimes as a 'theoretical physicist who revolutionized telecommunication.' You can read his obituary in the @LondonMathSoc newsletter at: bit.ly/2XeTrvn #DIASdiscovers
The @IrishResearch Advanced Laureate Awards are crucial for frontier basic research #LoveIrishResearch #DIASdiscovers twitter.com/IrishResearch/…