Tuesday, October 21st, 2025
Workshop: Linden Disney-Hogg
Time: 9:30 AM - 10:30 AM
Location: SCGP 102
Title: Symmetry, integrability and computation of hyperbolic monopole curves
Speaker: Linden Disney-Hogg
Abstract: The spectral curves of hyperbolic monopoles are a powerful tool to leverage the techniques of algebraic geometry to gain insight. By reviewing the connections to instantons, Euclidean monopoles, and other integrable systems I will describe what is known so far, as well as muse on what is still to come. This is based on joint work with Harry Braden and Derek Harland.
Title: Symmetry, integrability and computation of hyperbolic monopole curves
Speaker: Linden Disney-Hogg
Abstract: The spectral curves of hyperbolic monopoles are a powerful tool to leverage the techniques of algebraic geometry to gain insight. By reviewing the connections to instantons, Euclidean monopoles, and other integrable systems I will describe what is known so far, as well as muse on what is still to come. This is based on joint work with Harry Braden and Derek Harland.
Workshop: Derek Harland
Time: 11:00 AM - 12:00 PM
Location: SCGP 102
Title: L2 and Twistor Metrics for Hyperbolic Monopoles
Speaker: Derek Harland
Abstract: It is well-known that the L2 metric on the moduli space of hyperbolic monopoles, defined using a Coulomb gauge fixing condition, diverges. Recently we found a solution to this problem using a supersymmetry-inspired gauge-fixing condition. This talk will review this construction, and compare it with structures introduced by Nash and Bielawski–Schwachh¨ofer using twistor theory. It will present results of ongoing calculations of these metrics. This is joint work with Linden Disney-Hogg, Guido Franchetti and Thomas Galvin.
Title: L2 and Twistor Metrics for Hyperbolic Monopoles
Speaker: Derek Harland
Abstract: It is well-known that the L2 metric on the moduli space of hyperbolic monopoles, defined using a Coulomb gauge fixing condition, diverges. Recently we found a solution to this problem using a supersymmetry-inspired gauge-fixing condition. This talk will review this construction, and compare it with structures introduced by Nash and Bielawski–Schwachh¨ofer using twistor theory. It will present results of ongoing calculations of these metrics. This is joint work with Linden Disney-Hogg, Guido Franchetti and Thomas Galvin.
Program Talk: Leonard Susskind
Time: 11:15 AM - 12:15 PM
Location: SCGP 313
Title: TBA
Speaker: Leonard Susskind
Abstract: N/A
Title: TBA
Speaker: Leonard Susskind
Abstract: N/A
Workshop: Daniel Fadel
Time: 2:30 PM - 3:30 PM
Location: SCGP 102
Title: Energy Concentration and Min-Max Solutions in SU(2) Yang–Mills–Higgs Theory with Arbitrary Positive Coupling Constant
Speaker: Daniel Fadel
Abstract: I will present recent joint work with Da Rong Cheng (Miami) and Luiz Lara (Unicamp) on the SU(2) Yang–Mills–Higgs functional with arbitrary positive coupling constant over oriented Riemannian 3-manifolds. Motivated by Pigati–Stern’s work on the abelian case, we introduce a scaling parameter and study sequences of critical points under natural energy bounds, proving that as the parameter tends to zero, energy concentrates at finitely many points with the remaining energy captured by an L2 harmonic 1-form. Around each concentration point, finitely many non-trivial “bubbles” arise on R3, and an energy gap plus a no-neck result guarantee that the total concentrated energy equals the sum of the bubble energies. On closed 3-manifolds, we adapt Pigati–Stern’s min–max construction to the SU(2) setting to produce non-trivial critical points for sufficiently small parameter values, ensuring bubbling on rational homology 3-spheres and thus the existence of non-trivial critical points on R3. I will conclude with open questions, higher-dimensional extensions, and connections with problems such as the large-mass limit of G2-monopoles.
Title: Energy Concentration and Min-Max Solutions in SU(2) Yang–Mills–Higgs Theory with Arbitrary Positive Coupling Constant
Speaker: Daniel Fadel
Abstract: I will present recent joint work with Da Rong Cheng (Miami) and Luiz Lara (Unicamp) on the SU(2) Yang–Mills–Higgs functional with arbitrary positive coupling constant over oriented Riemannian 3-manifolds. Motivated by Pigati–Stern’s work on the abelian case, we introduce a scaling parameter and study sequences of critical points under natural energy bounds, proving that as the parameter tends to zero, energy concentrates at finitely many points with the remaining energy captured by an L2 harmonic 1-form. Around each concentration point, finitely many non-trivial “bubbles” arise on R3, and an energy gap plus a no-neck result guarantee that the total concentrated energy equals the sum of the bubble energies. On closed 3-manifolds, we adapt Pigati–Stern’s min–max construction to the SU(2) setting to produce non-trivial critical points for sufficiently small parameter values, ensuring bubbling on rational homology 3-spheres and thus the existence of non-trivial critical points on R3. I will conclude with open questions, higher-dimensional extensions, and connections with problems such as the large-mass limit of G2-monopoles.
Workshop: Saman Habibi Esfahani
Time: 4:00 PM - 5:00 PM
Location: SCGP 102
Title: Fueter Sections and Z2-Harmonic 1-Forms
Speaker: Saman Habibi Esfahani
Abstract: I will discuss Fueter sections of monopole bundles over 3-manifolds and related compactness problems, which arise in the study of monopoles and calibrated geometry on Calabi–Yau 3-folds and G2-manifolds. Taubes suggested that counting Fueter sections of monopole bundles on 3-manifolds could lead to new 3-manifold invariants, while Donaldson and Segal proposed counting them over special Lagrangians to define invariants of Calabi–Yau 3-folds. Similar problems also appear in the study of the space of coassociatives in G2 geometry. The central question in all of these proposals is whether the space of Fueter sections is compact. We address this question in certain cases, proving and disproving several conjectures in the field and, in particular, answering a question raised by Taubes in 1999. A key observation is that Z2-harmonic forms play a crucial role in the problem. This talk is based on joint work with Yang Li.
Title: Fueter Sections and Z2-Harmonic 1-Forms
Speaker: Saman Habibi Esfahani
Abstract: I will discuss Fueter sections of monopole bundles over 3-manifolds and related compactness problems, which arise in the study of monopoles and calibrated geometry on Calabi–Yau 3-folds and G2-manifolds. Taubes suggested that counting Fueter sections of monopole bundles on 3-manifolds could lead to new 3-manifold invariants, while Donaldson and Segal proposed counting them over special Lagrangians to define invariants of Calabi–Yau 3-folds. Similar problems also appear in the study of the space of coassociatives in G2 geometry. The central question in all of these proposals is whether the space of Fueter sections is compact. We address this question in certain cases, proving and disproving several conjectures in the field and, in particular, answering a question raised by Taubes in 1999. A key observation is that Z2-harmonic forms play a crucial role in the problem. This talk is based on joint work with Yang Li.