## Status:

I am a Postdoctoral Research Assistant in Geometry and Analysis working with Professor Dominic Joyce in Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics.

## Personal website:

## ORCID iD:

https://orcid.org/0000-0003-3403-8536## Research groups:

## Address

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

## Recent Publications:

On orientations for gauge-theoretic moduli spaces

Advances in Mathematics
volume 326
page 106957-
(9 January 2020)

Vafa-Witten invariants for projective surfaces I: stable case

Journal of Algebraic Geometry
page 1-1
(23 October 2019)

A perturbation and generic smoothness of the Vafa-Witten moduli spaces on closed symplectic four-manifolds

Glasgow Mathematical Journal
issue 2
volume 61
page 471-486
(13 July 2018)

On the singular sets of solutions to the Kapustin–Witten equations and the Vafa–Witten ones on compact Kähler surfaces

Geometriae Dedicata
issue 1
volume 199
page 177-187
(1 March 2018)

Vafa-Witten invariants for projective surfaces II: semistable case

Pure and Applied Mathematics Quarterly
issue 3
volume 13
page 517–562-
(1 January 2018)

Some boundedness properties of solutions to the Vafa–Witten equations on closed 4-manifolds

Quarterly Journal of Mathematics
issue 4
volume 68
page 1203-1225
(12 April 2017)

Stable sheaves with twisted sections and the Vafa-Witten equations on smooth projective surfaces

MANUSCRIPTA MATHEMATICA
issue 3-4
volume 146
page 351-363
(March 2015)
Full text available

A removal singularity theorem of the Donaldson-Thomas instanton on compact Kahler threefolds

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
issue 1
volume 411
page 422-428
(1 March 2014)
Full text available

A weak compactness theorem of the Donaldson-Thomas instantons on compact Kahler threefolds

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
issue 1
volume 408
page 27-34
(1 December 2013)
Full text available

A construction of Spin(7)-instantons

Annals of Global Analysis and Geometry
issue 4
volume 42
page 495-521
(12 April 2012)

## Research interests:

Gauge Theory, Geometric Analysis, Algebraic Geometry

My current research interests are in the Vafa-Witten theory and Kapustin-Witten one, and their relations with gauge theories in higher dimensions such as Donaldson-Thomas theory, G_2 instantons and Spin(7)-instantons.

## Teaching:

- Introduction to Gauge Theory, TCC course, Trinity 2019.
- Tutor in Linear Algebra I, Wycliffe Hall, Hilary 2019.
- Tutor in Analysis II, St Edmund Hall, Hilary 2019.
- Tutor in Topology, St Edmund Hall, Hilary 2019.
- Tutor in Linear Algebra I, Wycliffe Hall, Michaelmas 2018.
- Tutor in C3.7 Elliptic Curves, Michaelmas 2018.
- Intercollegiate class tutor in B3.2 Geometry of Surfaces, Michaelmas 2018.
- Consultation sessions in B3.3 Algebraic Curves, Trinity 2018.
- Intercollegiate class tutor in B3.3 Algebraic Curves, Hilary 2018.

## Major / recent publications:

- D. Joyce, Y. Tanaka and M. Upmeier, On orientations for gauge-theoretic moduli spaces, Adv. Math. 362 (2020), 106957.
- Y. Tanaka and R. P. Thomas, Vafa-Witten invariants for projective surfaces I: stable case, to appear in Journal of Algebraic Geometry.
- Y. Tanaka, A perturbation and generic smoothness of the Vafa-Witten moduli spaces on closed symplectic four-manifolds, Glasg. Math. J. 61 (2019), 471-486.
- Y. Tanaka, On the singular sets of solutions to the Kapustin-Witten equations and the Vafa-Witten ones on compact Kahler surfaces, Geom. Dedicata 199 (2019), 177-187.
- Y. Tanaka and R. P. Thomas, Vafa-Witten invariants for projective surfaces II: semistable case, Pure Appl. Math. Q. 13 (2017), 517-562, Special Issue in Honor of Simon Donaldson.
- Y. Tanaka, Some boundedness properties of solutions to the Vafa-Witten equations on closed 4-manifolds, Q. J. Math. 68 (2017), 1203-1225.
- Y. Tanaka, On the moduli space of the Donaldson-Thomas instanton, Extracta Math. 31 (2016), 89-107.
- Y. Tanaka, Stable sheaves with twisted sections and the Vafa-Witten equations on smooth projective surfaces, Manuscripta Math. 146 (2015), 351-363.
- Y. Tanaka, A removal singularity theorem of the Donaldson-Thomas instantons on compact Kahler threefolds, J. Math. Anal. and Appl. 411 (2014), 422-428.
- Y. Tanaka, A weak compactness theorem of the Donaldson-Thomas instantons on compact Kahler threefolds, J. Math. Anal. and Appl. 408 (2013), 27-34.
- Y. Tanaka, A construction of Spin(7)-instantons, Ann. Global Anal. Geom. 42 (2012), 495-521.