Page 357 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 357
GEOMETRIC ANALYSIS AND LOW-DIMENSIONAL TOPOLOGY (MS-59)
information of X and may be equipped with a pairing on DH1(F ) that corresponds to the
intersection pairing of X. This construction also works for closed surfaces.
A Brakke type regularity for the Allen-Cahn flow
Shengwen Wang, shengwen.wang@qmul.ac.uk
Queen Mary University of London, United Kingdom
Coauthor: Huy Nguyen
We will talk about an analogue of the Brakke’s local regularity theorem for the parabolic
Allen-Cahn equation. In particular, we show uniform C2,α regularity for the transition layers
converging to smooth mean curvature flows as tend to 0 under the almost unit-density as-
sumption. This can be viewed as a diffused version of the Brakke regularity for the limit mean
curvature flow. This talk is based on joint work with Huy Nguyen.
Algebraic and geometric classification of Yang-Mills-Higgs flow lines
Graeme Wilkin, graeme.wilkin@york.ac.uk
University of York, United Kingdom
The Yang-Mills-Higgs flow on a compact Riemann surface is modelled on a nonlinear heat
equation, and therefore existence of the reverse flow is problematic in general. In this talk I will
explain how the existence of a certain filtration (analogous to the Harder-Narasimhan filtration,
but with the opposite inequality on the slopes) means that one can gauge the initial condition
so that the reverse flow exists for all time. This leads to an algebraic classification of flow lines
between pairs of critical points. A refinement of these ideas leads to a geometric classification
of flow lines in terms of certain secant varieties, which can then be used to distinguish between
broken and unbroken flow lines.
355
information of X and may be equipped with a pairing on DH1(F ) that corresponds to the
intersection pairing of X. This construction also works for closed surfaces.
A Brakke type regularity for the Allen-Cahn flow
Shengwen Wang, shengwen.wang@qmul.ac.uk
Queen Mary University of London, United Kingdom
Coauthor: Huy Nguyen
We will talk about an analogue of the Brakke’s local regularity theorem for the parabolic
Allen-Cahn equation. In particular, we show uniform C2,α regularity for the transition layers
converging to smooth mean curvature flows as tend to 0 under the almost unit-density as-
sumption. This can be viewed as a diffused version of the Brakke regularity for the limit mean
curvature flow. This talk is based on joint work with Huy Nguyen.
Algebraic and geometric classification of Yang-Mills-Higgs flow lines
Graeme Wilkin, graeme.wilkin@york.ac.uk
University of York, United Kingdom
The Yang-Mills-Higgs flow on a compact Riemann surface is modelled on a nonlinear heat
equation, and therefore existence of the reverse flow is problematic in general. In this talk I will
explain how the existence of a certain filtration (analogous to the Harder-Narasimhan filtration,
but with the opposite inequality on the slopes) means that one can gauge the initial condition
so that the reverse flow exists for all time. This leads to an algebraic classification of flow lines
between pairs of critical points. A refinement of these ideas leads to a geometric classification
of flow lines in terms of certain secant varieties, which can then be used to distinguish between
broken and unbroken flow lines.
355
