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Ollie Thakar

Publications and source records attributed to Ollie Thakar.

4 recordsLinked to original sources
arXiv2026

Entropy-Minimizing Diffeomorphisms on a $G_2$-Manifold

In this paper, we construct infinitely many diffeomorphisms of a Joyce manifold $M$ which achieve Yomdin's homological lower bound for topological entropy, imitating a recent construction of Farb-Looijenga for K3 surfaces. Moreover, following a recent paper by Crowley-Goette-Hertl, we show these diffeomorphisms act freely on a connected component of the Teichmüller space of $G_2$ structures on $M$, and hence that the homotopy moduli space of $G_2$ structures on $M$ has infinite fundamental group. We also discuss a putative analogy between dynamics on a $G_2$ manifold and that of an algebraic surface, and prove a theorem about its limitations.

math.DG↗
arXiv2025

The moduli space of multi-monopoles on a Riemann surface

We study the moduli space of solutions to the Seiberg-Witten equations with $N$ spinors on a compact Riemann surface. These moduli spaces arise in a program to define a new enumerative invariant of 3-manifolds. They are also of independent interest in the geometry of algebraic curves, as they parameterize generalized divisors in Brill-Noether theory for higher rank vector bundles. We compute the Euler characteristic of these spaces, completing a computation initiated by Doan, and then compute their rational homology using spectral curves and techniques of Fulton and Lazarsfeld.

math.DG↗
arXiv2023

Left-orderable surgeries on the knot $6_2$ via hyperbolic $\widetilde{PSL}(2,\mathbb{R})$-representations

We introduce a new method of detecting when the fundamental group of a Dehn surgery on a knot admits a left-ordering, a method which is particularly useful for 2-bridge knots. As an illustration of this method, we show that all Dehn surgeries on the knot $6_2$ with slope in the interval $(-4, 8)\cap\mathbb{Q}$ have left-orderable fundamental groups by exhibiting a family of hyperbolic $\widetilde{PSL}(2,\mathbb{R})$-representations of the knot complement group.

math.GT↗