Research Interests:
Geometry from Physics, Mathematics from/for Theoretical Neuroscience
- o Differential Geometry.
- o Complex Geometry.
- o Partial Differential Equations.
- o Gauge Theory.
- o Mathematical Physics.
- o Mathematical Biology.
Papers and Preprints:
- o R. Conlon, A. Degeratu, F. Rochon: Quasi-asymptotically conical Calabi-Yau manifolds, arXiv preprint 2016.
- o K. Morrison, A. Degeratu, V. Itskov, C. Curto:
Diversity of emergent dynamics in competitive threshold-linear networks: a preliminary report,
arXiv preprint 2016.
- o A. Degeratu, T. Walpuski: Rigid HYM connections on tautological bundles over ALE crepant resolutions in dimension three,
SIGMA 12 (2016), 017, 23 pages; doi:10.3842/SIGMA.2016.017.
- o A. Degeratu, R. Mazzeo: Fredholm theory for
elliptic operators on quasi-asymptotically conical spaces,
arXiv preprint 2014.
- o C. Curto, A. Degeratu, V. Itskov: Encoding
binary patterns of neural activity in networks of
threshold-linear neurons, Neural Computation, Volume 25 (2013), pp
2858-2903;
doi:10.1162/NECO_a_00504,
arXiv preprint 2012.
- o A. Degeratu, M. Stern: Witten spinors on
nonspin manifolds, Communications in
Mathematical Physics, Volume 324, Issue 2 (2013), pp 301-350;
doi:10.1007/s00220-013-1804-0,
arXiv preprint 2011.
- o C. Curto, A. Degeratu, V. Itskov: Flexible memory
networks, Bulletin of Mathematical Biology,Volume 74 (2012),
pp 590-614;
doi:10.1007/s11538-011-9678-9,
arXiv preprint 2010,
SfN Poster.
- o A. Degeratu, K. Wendland: Friendly giant meets
pointlike instantons? On a new conjecture by John McKay,
in "Moonshine - The First Quarter Century and Beyond, A
Workshop on the Moonshine Conjectures and Vertex
Algebras", LMS Lecture Notes Series no. 372 (2010),
55-127;
Augsburg preprint number 037/2007.
- o A. Degeratu: Eta invariants from Molien series,
The Quarterly Journal of Mathematics Volume 60, Number
3 (2009); doi: 10.1093/qmath/han016,
[pdf].
- o A. Degeratu, M. Stern: The Positive Mass
Conjecture for non-spin manifolds; math.DG/0412151
(has a sign error in Proposition 6.5).
- o A.Degeratu: Flops of Crepant Resolutions,
Turkish J. Math. 28 (2004), no. 1, 23--40 (Proceedings
ofthe 10th Gokova Geometry and Topology Conference);
[pdf].
- o A. Degeratu: Geometrical McKay Correspondence
for Isolated Singularities; math.DG/0302068.
- o My PhD thesis: Eta Invariants and Molien series for
Unimodular groups, MIT 2001; [pdf].
Posters:
- o K. Morrison, A. Degeratu, V. Itskov, C. Curto: Pattern Generation in Simple Inhibition-Dominated Networks, Cosyne poster (2016).
- o
C. Curto, A. Degeratu, V. Itskov: Perturbative memory encoding in recurrent networks,
Cosyne Poster (2012).
- o
C. Curto, A. Degeratu, V. Itskov: Recurrent vs
feedforward networks: differences in neural code topology,
Cosyne Poster (2012).
- o
C. Curto, A. Degeratu, V. Itskov:
Flexible memory networks,
Cosyne Poster (2010).
Miscellanea:
- o A.Degeratu: Singular spin structures and Witten
spinors; Oberwolfach Report for the Workshop "Stratified
spaces: Joining Analysis, Topology and Geometry",
December 11 - 17, 2011;
- o "Mini-Workshop: Higher Dimensional Elliptic
Fibrations", Abstracts from the mini-workshop held
October 3 - 9, 2010; Organized by Gavin Brown, Anda
Degeratu and Katrin Wendland, Oberwolfach Reports Vol. 7
(2010), no. 4, 2651 - 2680.
- o A.Degeratu: Fredholm theory on
quasi-asymptotically conical manifolds, Oberwolfach
Report for the Workshop "Analysis and Geometric
Singularities", August 19 - 25, 2007;
[pdf].
- o A.Degeratu: On the positive mass conjecture in
higher dimensions, Oberwolfach Report for the Workshop "Mathematical
Aspects of General Relativity", January 8 - 14, 2006;
[pdf].
- o A.Degeratu: Geometrical McKay correspondence,
Oberwolfach Report for the MiniWorkshop "Finite Groups",
May 16 - 22, 2004; [pdf].
- o A. Degeratu: Crepant resolutions of Calabi-Yau
orbifolds, Oberwolfach Report for the MiniWorkshop "Geometry
and Duality in String Theory", May 16 - 22 , 2004;
[pdf].
- o A. Degeratu, M. Haskins: Open problems in
L^2-cohomology [pdf];
notes written for the AIM workshop L^2-harmonic
forms in geometry and physics.
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