Windes Emily Autumn

Emily Autumn Windes is a mathematics researcher specializing in differential geometry, with a particular focus on manifolds with special holonomy and gauge theory in higher dimensions. She is currently completing her Ph.D. in Mathematics at the University of Oregon (expected 2025), where she works under the supervision of Boris Botvinnik (University of Oregon) and Aleksander Doan (University College London). Emily’s research contributions include work on special Lagrangian submanifolds, instantons, and calibrated geometry.

Differential geometry

Manifolds with special holonomy (G₂, Spin(7))

Gauge theory in higher dimensions

Special Lagrangian submanifolds

Calibrated geometry

Ph.D. Mathematics, University of Oregon, Expected 2025

1. Advisors: Boris Botvinnik, Aleksander Doan

M.A. Mathematics, University of Rochester, 2022

B.A. Honors Mathematics, University of Rochester, 2017

1. Senior Thesis: The Frobenius Theorem

B.A. Honors Physics, University of Rochester, 2017

1. Senior Thesis: From Harmonic Oscillators to Fields

On Sp(n)-Instantons and the Fourier-Mukai Transform of Complex Lagrangians (with Jesse Madnick), submitted.

Transversality for Perturbed Special Lagrangian Submanifolds, to appear in Annals of Global Analysis and Geometry.

“Two-frame fields on simply-connected Spin(7) manifolds” (with Ustün Yildirim), Proceedings of the 12th ISAAC Congress, Aveiro, Portugal, 2019.

“The Moduli Space of Graphical Associative Submanifolds,” Université Libre de Bruxelles, May 2024.

“The Moduli Space of Graphical Associative Submanifolds,” Simons Collaboration Conference, Duke University, May 2024.

“The Moduli Space of Graphical Associative Submanifolds,” Oregon State University, April 2024.

“Special Lagrangians and Morse Theory,” Midwest Geometry Conference, Kansas State University, March 2023.

“Special Lagrangians and Morse Theory,” Geometry & Topology Seminar, Duke University, Sept 2023.

“Contact Structures on G₂-manifolds,” ISAAC Congress, University of Aveiro, Aug 2019.

University of Oregon

1. Instructor: MATH 112 (Elementary Functions), 2023–present
2. Workshop Leader: MATH 111 (College Algebra), 2022

University of Rochester

1. Instructor: MATH 164 (Multivariable Calculus), Summers 2020–2022
2. Teaching Assistant: MATH 164, MATH 200, MATH 265, MATH 440, MATH 174, MATH 453 (2017–2022)
3. Workshop Leader: MATH 161 (Calculus I), 2018
4. Private Tutor: High school calculus through advanced undergraduate geometry & topology

Jack and Peggy Borsting Award (2023)

John V. Leahy Memorial Award (2023)

Paul and Harriet Civin Memorial Award (2023)

University of Rochester Graduate Teaching Award (2020)