Page 361 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 361
GEOMETRIES DEFINED BY DIFFERENTIAL FORMS (MS-44)
1) the correspondence between parallel VCPs on a Riemannian manifold M and parallel almost
complex structures on a higher dimensional knot space over M endowed with a L2-metric,
which generalizes Brylinski’s, LeBrun’s, Henrich’s and Verbitsky’s results for the case that
S is a codimension 2 submanifold in M , and S = S1 or M is a torsion-free G2-manifold,
respectively; 2) the similarities between integrable complex structures on one hand and torsion-
free G2-and Spin(7)-structures on the other hand; 3) the construction of CR-twistor spaces over
G2-manifolds, due to Verbitsky, and its extension to Spin(7)-manifolds. My lecture is based
on my joint works with Domenico Fiorenza, Kotaro Kawai, Lorenz Schwachhöfer and Luca
Vitagliano.
Special Lagrangians and Bridgeland Stability Conditions
Goncalo Oliveira, galato97@gmail.com
Universidade Federal Fluminense, Portugal
Coauthor: Jason Lotay
Building on conjectures of Richard Thomas and Shing-Tung-Yau, together with the definition
of Bridgeland stability conditions, Dominic Joyce proposed to use Lagrangian mean curva-
ture flow to “decompose” certain Lagrangian submanifolds into a combination of special La-
grangians. I will report on joint work in progress with Jason Lotay to prove parts of Joyce’s
program for certain symmetric hyperKahler 4-manifolds. Our work provides concrete geomet-
ric interpretations for many algebraic notions related to Bridgeland stability conditions.
Complex volume forms, totally real submanifolds and convexity
Tommaso Pacini, tommaso.pacini@unito.it
University of Torino, Italy
Totally real submanifolds play a natural role at the intersection between symplectic and complex
geometry. I will survey recent results in this direction, emphasizing relationships with the (anti-
)canonical bundle and with pluri-subharmonic functions.
The heterotic G2 system on contact Calabi–Yau 7-manifolds
Henrique Sá Earp, henrique.saearp@ime.unicamp.br
Unicamp, Brazil
We obtain non-trivial solutions to the heterotic G2 system, which are defined on the total spaces
of non-trivial circle bundles over Calabi–Yau 3-orbifolds. By adjusting the S1 fibres in propor-
tion to a power of the string constant α , we obtain a cocalibrated G2-structure the torsion of
which realises an arbitrary constant (trivial) dilaton field and an H-flux with nontrivial Chern–
Simons defect. We find examples of connections on the tangent bundle and a non-flat G2-
instanton induced from the horizontal Calabi–Yau metric which satisfy together the anomaly-
free condition, also known as the heterotic Bianchi identity. The connections on the tangent
bundle are G2-instantons up to higher order corrections in α .
359
1) the correspondence between parallel VCPs on a Riemannian manifold M and parallel almost
complex structures on a higher dimensional knot space over M endowed with a L2-metric,
which generalizes Brylinski’s, LeBrun’s, Henrich’s and Verbitsky’s results for the case that
S is a codimension 2 submanifold in M , and S = S1 or M is a torsion-free G2-manifold,
respectively; 2) the similarities between integrable complex structures on one hand and torsion-
free G2-and Spin(7)-structures on the other hand; 3) the construction of CR-twistor spaces over
G2-manifolds, due to Verbitsky, and its extension to Spin(7)-manifolds. My lecture is based
on my joint works with Domenico Fiorenza, Kotaro Kawai, Lorenz Schwachhöfer and Luca
Vitagliano.
Special Lagrangians and Bridgeland Stability Conditions
Goncalo Oliveira, galato97@gmail.com
Universidade Federal Fluminense, Portugal
Coauthor: Jason Lotay
Building on conjectures of Richard Thomas and Shing-Tung-Yau, together with the definition
of Bridgeland stability conditions, Dominic Joyce proposed to use Lagrangian mean curva-
ture flow to “decompose” certain Lagrangian submanifolds into a combination of special La-
grangians. I will report on joint work in progress with Jason Lotay to prove parts of Joyce’s
program for certain symmetric hyperKahler 4-manifolds. Our work provides concrete geomet-
ric interpretations for many algebraic notions related to Bridgeland stability conditions.
Complex volume forms, totally real submanifolds and convexity
Tommaso Pacini, tommaso.pacini@unito.it
University of Torino, Italy
Totally real submanifolds play a natural role at the intersection between symplectic and complex
geometry. I will survey recent results in this direction, emphasizing relationships with the (anti-
)canonical bundle and with pluri-subharmonic functions.
The heterotic G2 system on contact Calabi–Yau 7-manifolds
Henrique Sá Earp, henrique.saearp@ime.unicamp.br
Unicamp, Brazil
We obtain non-trivial solutions to the heterotic G2 system, which are defined on the total spaces
of non-trivial circle bundles over Calabi–Yau 3-orbifolds. By adjusting the S1 fibres in propor-
tion to a power of the string constant α , we obtain a cocalibrated G2-structure the torsion of
which realises an arbitrary constant (trivial) dilaton field and an H-flux with nontrivial Chern–
Simons defect. We find examples of connections on the tangent bundle and a non-flat G2-
instanton induced from the horizontal Calabi–Yau metric which satisfy together the anomaly-
free condition, also known as the heterotic Bianchi identity. The connections on the tangent
bundle are G2-instantons up to higher order corrections in α .
359
