Department of Mathematics

College of Arts and Sciences

University of Nebraska - Lincoln

**Short Bio:**
I am currently a postdoctoral faculty in mathematics at the University of Nebraska-Lincoln; my mentor is
Christine Kelley.
I recieved my PhD degree in mathematics from University of Kentucky in 2019
under the supervision of Heide Gluesing-Luerssen.
Before joining UNL, I was a postodcoral researcher at Aalto University,
working under the supervision of Olav Tirkkonen.

**Email:** name(dot)lastname(at)unl(dot)edu

**Visiting Address:** 238 Avery Hall

My research interests are in applied algebra, very broadly defined. Currently I am focused on applications to coding theory, quantum computation, wireless communications, and online privacy and security. This involves work with finite algebraic structures, which may be directly involved in said applications, or that may arise as discretized versions of continuous algebraic structures. I routinely use tools from finite field theory, Fourier analysis, representation theory, (finite or complex) Grassmannian geometry, and finite symplectic geometry. Check out my research statement and publications for more!

- Linear Algebra (MATH 314)

**T. Pllaha**, K. Volanto, O. Tirkkonen,**Decomposition of Clifford Gates**, To appear*In 2021 IEEE Global Communications Conference*.**Preprint**.- R. Vehkalahti,
**T. Pllaha**, O. Tirkkonen,**Signature Code Design for Fast Fading Channels**,*In 2021 IEEE International Symposium on Information Theory*, pp. 2936-2941, 2021. - M. Allaix, L. Holzbaur,
**T. Pllaha**, C. Hollanti,**High-Rate Quantum Private Information Retrieval with Weakly Self-Dual Star Product Codes**,*In 2021 IEEE International Symposium on Information Theory*, pp. 1046-1051, 2021. - R. Vehkalahti, J. Liao,
**T. Pllaha**, W. Han, O. Tirkkonen,**CSI Quantization for FDD Massive MIMO Communication**,*In 2021 IEEE Vehicular Technology Conference - Spring*.DOI:10.1109/VTC2021-Spring51267.2021.9449010. - R. Vehkalahti,
**T. Pllaha**, O. Tirkkonen,**Towards Ultra-Reliable Signature Coding with Multiple Transmit Antennas**,*In 2021 IEEE Vehicular Technology Conference - Spring*.DOI:10.1109/VTC2021-Spring51267.2021.9448780 . **T. Pllaha**, N. Rengaswamy, O. Tirkkonen, R. Calderbank,**Un-Weyl-ing the Clifford Hierarchy**,*Quantum*, vol. 4, no. 370, December 2020 (13 pages, double column).- M. Allaix, L. Holzbaur,
**T. Pllaha**, C. Hollanti,**Quantum Private Information Retrieval From Coded and Colluding Servers**,*IEEE Journal on Selected Areas in Information Theory*, pp. 1(2), 599-610, August 2020. **T. Pllaha**, O. Tirkkonen, R. Calderbank,**Reconstruction of Multi-user Binary Subspace Chirps**,*In 2020 IEEE International Symposium on Information Theory*, pp. 531-536.- M. Allaix, L. Holzbaur,
**T. Pllaha**, C. Hollanti,**Quantum Private Information Retrieval from MDS-coded and Colluding Servers**,*In 2020 IEEE International Symposium on Information Theory*, pp. 1059-1064. **T. Pllaha**,**Symplectic Isometries of Stabilizer Codes**,*Journal of Algebra and its Applications*, 19(2):2050021, 2020 (22 pages).- H. Gluesing-Luerssen,
**T. Pllaha**,**On Quantum Stabilizer Codes Derived from Local Frobenius Rings**,*Finite Fields and Their Applications*, 58, 2019, pp. 145-173. - H. Gluesing-Luerssen,
**T. Pllaha**,**Extension Theorems for Various Weight Functions over Frobenius Bimodules**,*Journal of Algebra and its Applications*, 17(3):1850052, 2018 (28 pages). **T. Pllaha**,**Equivalence of Classical and Quantum Codes**,*PhD Thesis, University of Kentucky*, February 2019.

- M. Allaix, S. Song, L. Holzbaur,
**T. Pllaha**, M. Hayashi, C. Hollanti,**On the Capacity of Quantum Private Information Retrieval from MDS-Coded and Colluding Servers**,**Preprint**. **T. Pllaha**, E. Heikkilä, R. Calderbank, O. Tirkkonen,**Low-Complexity Grassmannian Quantization Based on Binary Chirps**,**Preprint**.**T. Pllaha**, O. Tirkkonen, R. Calderbank,**Binary Subspace Chirps**,**Preprint**.- M. Meyer,
**T. Pllaha**,**Laplacian Simplices II: A Coding Theoretic Approach**,**Preprint**.