Books  

1. I. G. Avramidi, Heat Kernel on Lie Groups and Maximally Symmetric Spaces, (Springer/Birkhaeuser, 2023)     

2. I. G. Avramidi, Heat Kernel Method and Its Applications, (Springer/Birkhaeuser, 2015)     

3. I. G. Avramidi, Heat Kernel and Quantum Gravity, (Berlin: Springer, 2000) 

Refereed Publications 

1. I. G. Avramidi and R. Niardi, MOND via matrix general relativity, Physica Scripta 99 (2024) 035244; Preprint: arXiv:2309.14270 [gr-qc]  

2. I. G. Avramidi, Spectral asymptotics of elliptic operators on manifolds, Reviews in Mathematical Physics (2024), Preprint: arXiv:2301.08728 [math-ph]

3. I. G. Avramidi, Heat semigroups on Weyl algebra,  Journal of Geometry and Physics, 161 (2021) 104044

4. I. G. Avramidi, Bogolyubov invariant via relative spectral invariants on manifolds, Journal of Mathematical Physics, 61 (2020) 032303

5. I. G. Avramidi, Relative spectral invariants of elliptic operators on manifolds, Journal of Geometry and Physics, 150 (2020) 103599

6. I. G. Avramidi, Quantum heat traces, Journal of Geometry and Physics, 112 (2017) 271-288

7. I. G. Avramidi and B. J. Buckman, Heat determinant on manifolds, Journal of Geometry and Physics, 104 (2016) 64-88

8. I. G. Avramidi and S. Collopy, One-loop quantum gravity in Einstein Universe, Journal of High Energy Physics, 11 (2015) 193

9. I. G. Avramidi, Heat trace and functional determinant in one dimension, Journal of Mathematical Physics 55 (2014) 123501

10. I. G. Avramidi and S. Collopy, Thermal Yang-Mills theory in Einstein Universe, Journal of Physics A: Mathematical and Theoretical, 45 (2012) 374009

11. I. G. Avramidi and S. Collopy, Effective action and phase transitions in thermal Yang-Mills theory on spheres, Communications in Mathematical Physics 311 (2012) 713-753

12. I. G. Avramidi, Non-perturbative effective action in gauge theories and quantum gravity, Advances in Theoretical and Mathematical Physics 14 (2010) 309-333

13. I. G. Avramidi, Mathematical tools for calculation of the effective action in quantum gravity, in: New Paths Towards Quantum Gravity, Ed. B. Booss-Bavnbek, G. Esposito and M. Lesch, (Berlin, Springer, 2010), pp. 193-259

14. G. Fucci and I. G. Avramidi, On the gravitationally induced Schwinger mechanism, In: Proceedings of the International Conference "Quantum Field Theory under the Influence of External Conditions" (QFEXT09). Eds. K. A. Milton and M. Bordag (Singapore: World Scientific, 2010), pp. 485-491

15.  I. G. Avramidi and G. Fucci, Low-energy effective action in non-perturbative electrodynamics in curved spacetime, Journal of Mathematical Physics 50 (2009) 102302

16. I. G. Avramidi and G. Fucci, A model for the Pioneer anomaly, Canadian Journal of Physics 87 (2009) 1089–1093

17. I. G. Avramidi and G. Fucci, Non-perturbative heat kernel asymptotics on homogeneous Abelian bundles, Communications in Mathematical Physics 291 (2009) 543-577

18. I. G. Avramidi and G. Fucci,  Kinematics in matrix gravity, General Relativity and Gravitation, 41 (2009) 1407-1435

19.  G. Fucci and I. G. Avramidi, Non-commutative corrections in spectral matrix gravity, Classical and Quantum Gravity 26 (2009) 045019, 24pp

20. I. G. Avramidi, Heat kernel on homogeneous bundles over symmetric spaces,  Communications in Mathematical Physics, 288 (2009) 963-1006

21. G. Fucci and I. G. Avramidi, Non-commutative Einstein equations,  Classical and Quantum Gravity, 25 (2008) 025005  

22. I. G. Avramidi, Heat kernel on homogeneous bundles,  International Journal of Geometric Methods in Modern Physics, 5 (2008) 1-23 

23. I. G. Avramidi, Heat kernel asymptotics on symmetric spaces,  Proc. Midwest Geometry Conference, Communications in Mathematical Analysis, Conf. 01 (2008) 1–10

24. I. G. Avramidi, Non-Laplace type operators on manifolds with boundary, in: Analysis, Geometry and Topology of Elliptic Operators, Papers in Honor of Krzysztof P. Wojciechowski, Eds. B. Booss-Bavnbek, S. Klimek, M. Lesch and W. Zhang (Singapore: World Scientific, 2006), pp. 119-152; by invitation

25. I. G. Avramidi, Dirac operator in matrix geometry, International Journal of Geometric Methods in Modern Physics, 2 (2005) 227-264,   (special issue dedicated to the memory of Dmitri Ivanenko and Vladimir Fock), by invitation 

26. I. G. Avramidi, A note on contributions of Prof. Minakshisundaram to mathematical physics, Proc. of Andhra Pradesh Akademi of Sciences, , 8 (2004), 247-248 (special issue dedicated to the memory of Subbaramiah Minakshisundaram), by invitation 

27. I. G. Avramidi, Gauged gravity via spectral asymptotics of non-Laplace type operators, Journal of High Energy Physics, 07 (2004) 030 

28. I. G. Avramidi, Heat kernel asymptotics of Zaremba boundary value problem, Mathematical Physics, Analysis and Geometry, 7 (2004) 9-46

29. I. G. Avramidi, Matrix general relativity: a new look at old problems, Classical and Quantum Gravity 21 (2004) 103-120 

30. I. G. Avramidi, A noncommutative deformation of general relativity, Physics Letters B 576 (2003) 195-198

31. I. G. Avramidi, Heat kernel approach in quantum field theory, Nuclear Physics Proc. Suppl. 104 (2002) 3-32  

32. I. G. Avramidi and T. Branson, A discrete leading symbol and spectral asymptotics for natural differential operators, Journal of Functional Analysis, 190 (2002) 292-337 

33. I. G. Avramidi and T. Branson, Heat kernel asymptotics of operators with non-Laplace principal part, Reviews in Mathematical Physics 13 (2001) 847-890 

34. I. G. Avramidi and R. Schimming, A new explicit expression for the Korteweg-De Vries hierarchy,  Mathematische Nachrichten, 219 (2000) 45-64 

35. I. G. Avramidi,  Covariant techniques for computation of the heat kernel,  Reviews in Mathematical Physics, 11 (1999) 947-980 

36. I. G. Avramidi and G. Esposito,  Gauge theories on manifolds with boundary,  Communications in Mathematical Physics 200 (1999) 495-543 

37. I. G. Avramidi,  One-loop effective potential in higher-dimensional Yang-Mills theory,   Fortschritte der Physik / Progress of Physics, 47 (1999) 4, 433-455 

38. I. G. Avramidi and G. Esposito,  Foundational Problems in Quantum Gravity, in: Recent Developments in General Relativity, Eds. A. Masielo et al. (Berlin: Springer, 1999), pp. 395-404 

39. I. G. Avramidi and G. Esposito, Heat kernel asymptotics of Gilkey-Smith boundary value problem, in: Trends in Mathematical Physics,  Eds. V. Alexiades and G. Siopsis, AMS/IP Studies in Advanced Mathematics, vol. 13, (American Mathematical Society and International Press, 1999), pp. 15-34

40. I. G. Avramidi and G. Esposito, On ellipticity and gauge invariance in Euclidean quantum gravity,   in: Trends in Mathematical Physics,  Eds. V. Alexiades and G. Siopsis, AMS/IP Studies in Advanced Mathematics, vol. 13, (American Mathematical Society and International Press, 1999), pp. 3-40

41. I. G. Avramidi,  Green functions of higher-order differential operators,  Journal of Mathematical Physics 39 (1998) 2889-2909 

42. I. G. Avramidi and G. Esposito,  Lack of strong ellipticity in Euclidean quantum gravity, Classical and Quantum Gravity 15 (1998) 1141-1152 

43. I. G. Avramidi,  Nonperturbative methods for calculating the heat kernel, in: Global Analysis, Differential Geometry and Lie Algebras, Ed. G. Tsagas, (Bucharest: Geometry Balkan Press, 1998), pp. 7-21

44. I. G. Avramidi and G. Esposito, New invariants in the one-loop divergences on manifolds with boundary, Classical and Quantum Gravity 15 (1998) 281-297 

45. I. G. Avramidi,  Covariant approximation schemes for calculation of the heat kernel in quantum field theory, in: Quantum Gravity,  Eds. V. A. Berezin, V. A. Rubakov and D. V. Semikoz, (Singapore: World Scientific, 1997), pp. 61-78

46. I. G. Avramidi,  Singularities of Green functions of the products of the Laplace-type operators, Physics Letters B 403 (1997) 280-284 

47. I. G. Avramidi, G. Esposito and A. Yu. Kamenshchik, Axial gauge in Euclidean quantum gravity, in: `Constrained Dynamics and Quantum Gravity 1996', Eds: V. de Alfaro, J. E. Nelson, G. Bandelloni, A. Blasi, M. Cavaglia' and A. T. Filippov, Nucl. Physics B Proceedings Supplement 57 (1997), pp. 245-246 

48. I. G. Avramidi, G. Esposito and A. Yu. Kamenshchik, Boundary operators in Euclidean quantum gravity, Classical Quantum Gravity 13 (1996) 2361-2373 

49. I. G. Avramidi,  A new algebraic approach for calculating the heat kernel in quantum gravity, Journal of Mathematical Physics 37 (1996) 374-394 

50. I. G. Avramidi and R. Schimming, Algorithms for the calculation of the heat kernel coefficients, in: `Quantum Field Theory under the Influence of External Conditions', Ed. M. Bordag, Teubner-Texte zur Physik, Band 30, (Stuttgart: Teubner, 1996), pp. 150-162

51. I. G. Avramidi, Covariant algebraic method for calculation of the low-energy heat kernel, Journal of Mathematical Physics 36 (1995) 5055-5070 

52. I. G. Avramidi and R. Schimming,  Heat kernel coefficients to the matrix Schroedinger operator, Journal of Mathematical Physics 36 (1995) 5042-5054 

53. I. G. Avramidi,  Covariant algebraic calculation of the one-loop effective potential in non-Abelian gauge theory and a new approach to stability problem, Journal of Mathematical Physics 36 (1995) 1557-1571  

54. I. G. Avramidi,  New algebraic methods for calculating the heat kernel and the effective action in quantum gravity and gauge theories, in: `Heat Kernel Techniques and Quantum Gravity', Ed. S. A. Fulling, Discourses in Mathematics and Its Applications, (College Station, Texas: Department of Mathematics, Texas A& M University, 1995), pp. 115-140

55. I. G. Avramidi,  The heat kernel on symmetric spaces via integrating over the group of isometries, Physics Letters B 336 (1994) 171-177  

56. I. G. Avramidi,  A new algebraic approach for calculating the heat kernel in gauge theories, Physics Letters B 305 (1993) 27-34  

57. I. G. Avramidi,  A method for calculating the heat kernel for manifolds with boundary,  Yadernaya Fizika 56 (1993) 245-252, [Russian]; Physics of Atomic Nucleus 56 (1993) 138-142 [English]  

58. I. G. Avramidi,  A covariant technique for the calculation of the one-loop effective action, Nuclear Physics B 355 (1991) 712-754  

59. I. G. Avramidi,  Gauge invariant theory of higher spin fields in curved space, International Journal of Modern Physics A 6 (1991) 1693-1700  

60. I. G. Avramidi,  The covariant technique for calculation of the heat kernel asymptotic expansion, Physics Letters B 238 (1990) 92-97  

61. I. G. Avramidi,  The nonlocal structure of one-loop effective action via partial summation of asymptotic expansion, Physics Letters B 236 (1990) 443-449  

62. I. G. Avramidi,  Covariant methods of studying the nonlocal structure of an effective action, Yadernaya Fizika, 49 (1989) 1185-1192, [Russian]; Soviet Journal of Nuclear Physics , 49 (1989) 735-739 [English]  

63. I. G. Avramidi,  Background field calculations in quantum field theory (vacuum polarization), Teoreticheskaya i Matematicheskaya Fizika, 79 (1989) 219-231, [Russian]; Theoretical and Mathematical Physics 79 (1989) 494-502 [English]  

64. I. G. Avramidi,  Asymptotic behavior of the quantum theory of gravity with higher order derivatives, Yadernaya Fizika, 44 (1986) 255-263, [Russian]; Soviet Journal of Nuclear Physics, 44 (1986) 160-164 [English]

65. I. G. Avramidi and A. O. Barvinsky, Asymptotic freedom in higher - derivative quantum gravity, Physics Letters B 159 (1985) 269-274  

66. I. G. Avramidi, B. G. Barabashov and G. G. Vertogradov, A method of reducing the effect of multipath propagation on the accuracy of determining the angles of arrival of radiowaves,  Radiotekhnika, 9 (1983) 69-72, [Russian]; Telecommunications and Radioengineering 9 (1983) 111-113 [English] 

Preprints, Reports and Thesis  

1. I. G. Avramidi, Analytic and Geometric Aspects of Heat Kenel Applications in Finance,   NATIXIS Corporate and Investment Bank, Paris, France, (2007), 249 pp. 

2. I. G. Avramidi and G. Esposito, Universal Functions in Euclidean Quantum Gravity, hep-th/9702150, 8 pp.  

3. I. G. Avramidi,  The heat kernel approach for calculating the effective action in quantum field theory and quantum gravity, University Greifswald (June, 1994), hep-th/9509077, 21 pp.  

4. I. G. Avramidi,  Covariant methods for calculating the low-energy effective action in quantum field theory and quantum gravity, University of Greifswald (March, 1994), gr-qc/9403036, 48 pp.  

5. I. G. Avramidi,  Covariant Methods for the Calculation of the Effective Action in Quantum Field Theory and Investigation of Higher-Derivative Quantum Gravity, PhD Thesis, Moscow State University (1986), Universal Decimal Code (UDC) 530.12:531.51, 178 pp. [Russian]; hep-th/9510140, 159 pp. [English]  

6. I. G. Avramidi,  Background field method in quantum theory, Moscow State University (1984), Deposited at VINITI (Soviet Institute for Scientific and Technical Information), No 1512-85 Dep., VINITI, Moscow, (1985), 41 pp., [in Russian] 

Conference Abstracts  

1. I. G. Avramidi, Noncommutative deformation of general relativity, in: International Congress of Mathematical Physics 2003, Lisbon, Book of Abstracts, (Lisbon, Portugal, 2003)  

2. I. G. Avramidi, Heat kernel asymptotics of Zaremba boundary value problem, in: International Congress of Mathematicians, Beijing 2002, Aug. 20-28, Abstracts of Short Communications and Poster Sessions, (Beijing: Higher Education Press, 2002), pp.~208--209   

3. I. G. Avramidi, Heat kernel asymptotics of a non-smooth boundary-value problem, in: International Congress of Mathematical Physics 2000, London, Book of Abstracts, (London, UK, 2000), p.~98   

4. I. G. Avramidi,  Heat kernel asymptotics of a non-smooth boundary-value problem, in: Abstracts of the International Conference `Workshop in Spectral Geometry', University of Bristol, Bristol, UK, 2000   

5. I. G. Avramidi,  Heat kernel asymptotics of operators with non-Laplace principl part, in: Abstracts of the International Conference `Workshop in Partial Differential Equations', University of Potsdam, Potsdam, Germany, 1999   

6. I. G. Avramidi,  Heat kernel asymptotics of the Gilkey-Smith boundary value problem, in: Abstracts of `8th International Conference on Differential Equations and Mathematical Phyics', University of Alabama, Birmingham, Alabama, 1999   

7. I. G. Avramidi,  Heat kernel as the basis for the functional integration in quantum field theory, in: Functional Integration: Basics and Applications, Eds: C. DeWitt-Morette, P. Cartier and A. Folacci, NATO ASI Series, Series B: Vol. 361, (New York: Plenum Press, 1997), p. 413-413   

8. I. G. Avramidi,  Effective potential in Yang-Mills theory and the stability of the chromomagnetic vacuum, in: `Quantum Field Theory under the Influence of External Conditions', Ed. M. Bordag, Teubner-Texte zur Physik, Band 30, (Stuttgart: Teubner, 1996), pp. 168-169   

9. I. G. Avramidi,  The low energy heat kernel and the effective action in semiclassical quantum gravity, Abstracts of 14th International Conference General "Relativity and Gravitation", Florence, August 6-12, 1995, 2 pp.   

10. I. G. Avramidi,  One-loop approximation in quantum theory of scalar, spinor and vector fields in external gravitational background field, in: Modern theoretical and experimental problems of general relativity and gravitation, Abstracts of VIth Soviet Gravitational Conference, Ed. V. N. Ponomarev (Moscow: Moscow State Pedagogical Institute (MGPI), 1984), pp. 199-201, [in Russian]  

Lecture Notes 

1. I. G. Avramidi, Problem of Quantum Gravity, New Mexico Tech, 2012, 15 pp

2. I. G. Avramidi, Lie Algebra SU(2), New Mexico Tech, 2011, 24 pp. 

3. I. G. Avramidi, Lie Algebra SL(2,C), New Mexico Tech, 2011, 6 pp. 

4. I. G. Avramidi, Heisenberg Algebra, New Mexico Tech, 2011, 6 pp. 

5. I. G. Avramidi, Riemannian Geometry and the Geometry of Lie Groups, New Mexico Tech, 2010, 70 pp.

6. I. G. Avramidi, Introduction to Differential Geometry, Lecture Notes for MATH 442, New Mexico Tech, 2005, 209 pp 

7. I. G. Avramidi, Linear Algebra and Vector Analysis, (can be used for MATH 332, MATH 454, MATH 442), New Mexico Tech, 2005, 118 pp. 

8. I. G. Avramidi, Basic Concepts of Analysis, Lecture Notes for MATH 372, New Mexico Tech, 2004, 127 pp. 

9. I. G. Avramidi, Basic Concepts of Mathematics, Lecture Notes for MATH 352, New Mexico Tech, 2004, 110 pp. 

10. I. G. Avramidi, Differential Forms, New Mexico Tech, 2003, 13 pp. 

11. I. G. Avramidi, Elementary Notes on Tensors, New Mexico Tech, 2001, 9 pp.

12. I. G. Avramidi, Functional Analysis, Lecture Notes for MATH 535, New Mexico Tech, 2005, 165 pp.  

13. I. G. Avramidi, Methods of Mathematical Physics, Lecture Notes for MATH 536, New Mexico Tech, 2000, 67 pp.

14. I. G. Avramidi, Notes on Asymptotic Expansions, Lecture Notes for MATH 536, New Mexico Tech, 2000, 49 pp.

15. I. G. Avramidi, Effective Action Approach to Quantum Field Theory, New Mexico Tech, 2000, 90 pp.  

16. I. G. Avramidi, Special Relativity and Quantum Fields, New Mexico Tech, 2000, 27 pp.  

17. I. G. Avramidi, Notes on Lie Groups, New Mexico Tech, 2000, 14 pp.  

18. I. G. Avramidi, Notes on Hilbert Spaces, New Mexico Tech, 2000, 17 pp.  

Books in preparation 

1.  I. G. Avramidi,  Heat Kernel in Mathematical Physics,