Russian Mathematical Surveys, 2025, Volume 80, Issue 4, Pages 733–741 DOI: https://doi.org/10.4213/rm10253e (Mi rm10253)

DOI: https://doi.org/10.4213/rm10253e

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On March 2, 2024, Yuri Gennadievich Prokhorov, corresponding member of the Russian Academy of Sciences (RAS), chief researcher at the Steklov Mathematical Institute of RAS, and professor at the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University, turned 60 years of age. He is widely recognized as one of the global leaders in contemporary birational algebraic geometry.

He was born in the town of Orekhovo–Zuevo in Moscow Oblast, in a family of engineers. While still in school, he demonstrated talents for the exact sciences, which in 1979 earned him an invitation to Boarding School No. 18, a physics-mathematics school affiliated with Moscow State University. After graduating successfully in 1981, he enrolled in the Faculty of Mechanics and Mathematics (Mechmat) at Moscow State University (MSU).

In the vibrant scientific atmosphere of Mechmat in the early 1980s, Yuri Prokhorov was fortunate to quickly find a mentor, Vasily Alekseevich Iskovskikh, who became his teacher, senior colleague, coauthor, and a kindred spirit in life principles. Thus Yuri joined the famous Soviet algebraic geometry school founded by I. R. Shafarevich.

One of the key research fronts during that period concerned birational geometry of special classes of three-dimensional algebraic varieties. These problems became the focus of Prokhorov’s work — initially under Iskovskikh’s guidance, and later, after his teacher’s untimely death, as the informal leader of the vibrant research community now known as the Iskovskikh School.

After defending his undergraduate thesis in 1986, Prokhorov continued research under Iskovskikh’s supervision in the graduate program at Mechmat, defending his Kandidat dissertation “Geometric properties of Fano varieties” in 1990. His teaching career began in 1989 with a position as assistant at Bauman Moscow State Technical University. In 1991 he joined the Department of Higher Algebra of MSU, rising to the rank of professor by 2005, after having defended his D.Sc. dissertation “Inductive methods in the theory of minimal models” in 2002. In 2012 the Department of Algebraic Geometry was organized at the Steklov Mathematical Institute, and since 2013 Prokhorov has been a member of that department, while continuing to serve as a professor at Mechmat. True to the tradition of his teacher, he remains actively engaged in lecturing, mentoring students, and leading the Iskovskikh Seminar.

One of the first problems in which Prokhorov got interested was the rationality question for algebraic varieties. In particular, he made significant advances in the study of Noether’s problem concerning the rationality of the quotients of projective spaces by finite groups. In his early papers [1], [3], and [4], together with I. Ya. Kolpakov-Miroshnichenko he showed that the quotients of three-dimensional projective space by certain complicated finite groups are rational. The proof was based on the study of equivariant birational transformations; this method was later used by Prokhorov in many other works, a tool he honed to perfection. In his subsequent papers Prokhorov returned several times to rationality questions for quotient varieties, in particular, jointly with experts in invariant theory [16], [24]. Multiple results concerning Noether’s problem were summarized in the survey [25].

Another circle of questions which Prokhorov began studying at the beginning of his career concerns the automorphism groups of Fano varieties. In one of his first papers [2] he described all smooth prime Fano threefolds of large genus which admit an action of an infinite group. Later he returned repeatedly to this problem, improving his previous results. In particular, in the joint work with A. G. Kuznetsov and C. A. Shramov [49], the finiteness of the automorphism groups of smooth prime Fano threefolds of small genus was proved using group actions on Hilbert schemes of lines and conics. In the joint work with Kuznetsov [48] the structure of smooth Fano threefolds of genus $12$ with an action of the multiplicative group of the field was described. In a series of other papers Prokhorov obtained results on the automorphism groups of singular del Pezzo surfaces [57] (with I. A. Cheltsov) and four-dimensional Fano–Mukai varieties [53], [66] (with M. G. Zaidenberg).

Prokhorov’s works made a great impact on the study of the birational automorphism groups of algebraic varieties and their finite subgroups. For instance, in [28], [37], and [52] he described $p$-subgroups of the birational automorphism groups of rationally connected threefolds. In [29] he classified finite non-abelian simple subgroups of such groups, and in [34] described involutions in the Cremona group of rank $3$, that is, in the birational automorphism group of three-dimensional projective space. In a joint work with F. A. Bogomolov [30] new obstructions to stable linearizability for subgroups of the Cremona group of rank $2$ were introduced; their study was continued in [40]. In a recent joint work with J. Blanc, Cheltsov, and A. Duncan [61] results concerning the genus and gonality of birational automorphisms of threefolds were obtained. Furthermore, Prokhorov worked on the classification of finite quasi-simple subgroups [67] and symmetric groups [70] in the Cremona group. He presented a detailed survey of results on birational automorphism groups and related questions at the European Congress of Mathematics in 2020; see [72].

A series of results due to Prokhorov on the Jordan property of birational and bimeromorphic automorphism groups deserves to be mentioned separately. The history of this question goes back to an old paper by C. Jordan which showed, among other things, that this property holds for the group of invertible matrices over the field of complex numbers. In the late 20th century W. Feit and É. Ghys asked whether or not it holds for the diffeomorphism groups of smooth compact manifolds, but a real breakthrough happened owing to J.-P. Serre, who proved that this property holds for the Cremona group of rank $2$ over a field of characteristic zero. Prokhorov, in the joint work with Shramov [44], showed that the Cremona group of any rank and, more generally, the birational automorphism group of an arbitrary rationally connected variety over a field of characteristic zero enjoys the Jordan property (the proof for rank $4$ and higher relied on the Borisov–Alexeev–Borisov conjecture, which was subsequently proved by C. Birkar). In their further works Prokhorov and Shramov established the Jordan property for the birational automorphism groups of non-uniruled varieties and varieties of zero irregularity [38], and also for the Cremona group of rank $2$ over a finite field [73]. In addition, they obtained a classification of three-dimensional varieties with Jordan birational automorphism groups [51], compact complex surfaces with Jordan bimeromorphic automorphism groups [60], and three-dimensional compact Kähler varieties with Jordan bimeromorphic automorphism groups [55], [65].

The geometry of conic bundles has been attracting Prokhorov’s attention since the end of the 1990s. He described the current state of this branch of algebraic geometry in the survey [50]. His main contribution to the field is the proof (with Sh. Mori [17], [18]) of the conjecture, due to V. A. Iskovskikh, that the base of a terminal three-dimensional $\mathbb Q$-conic bundle has only Du Val singularities. He also (jointly with Mori [19] checked the conjecture of M. Reid on the existence of an effective anticanonical divisor with Du Val singularities for such conic bundles. Subsequently, Prokhorov and Mori proceeded with the classification of singular fibres of three-dimensional $\mathbb Q$-conic bundles. These results, alongside with their ongoing generalizations for germs of extremal contractions of threefolds, can be found in [27], [42], [54], and [58]. A review of this series of works was given by Prokhorov in his talk at the International Congress of Mathematicians in 2022; see [71].

Another important direction of Prokhorov’s research is the geometry of $\mathbb Q$-Fano varieties. The main invariants of such a variety are its $\mathbb Q$-Fano index, which is the maximum integer dividing the anticanonical divisor in the Weil divisor class group, and the genus of the variety, which is defined by the anticanonical linear system. In the joint paper with Reid [43] Prokhorov established an upper bound of $4$ for the dimension of the half-anticanonical linear system of a $\mathbb Q$-Fano threefold of index $2$, and described all cases when this bound is attained. In his recent works [64] and [76] he proved the rationality of all $\mathbb Q$-Fano threefolds of index larger than $7$, and also for other large values of the index under certain additional assumptions. Apart from this, in [63] he studied $\mathbb Q$-Fano threefolds with no conic bundle structures.

In [13] Prokhorov proved an optimal upper bound of $72$ for the degree of Fano threefolds with canonical Gorenstein singularities, and described the unique example attaining this bound (it is interesting to mention that this example was known already to G. Fano). Another optimal result related to the Minimal Model Program is an upper bound of $125/2$ for the degree of terminal Fano threefolds whose Weil divisor class group has rank $1$; see [14]. The proof of this result uses the version, due to M. Reid, of the Riemann–Roch formula for $\mathbb Q$-Cartier divisors.

Prokhorov’s works on $G$-Fano varieties can be regarded as a continuation of results of Yu. I. Manin and Iskovskikh. In his first paper on this topic he classified $G$-del Pezzo threefolds (see [32]) and Gorenstein $G$-Fano threefolds of rank $1$ (see [33]). Thus, he found many new classes of Fano threefolds with large symmetry groups. This has applications to the problems of $G$-rationality and rationality for terminal Fano threefolds over algebraically non-closed fields. In recent joint papers Prokhorov and Kuznetsov obtained a nearly complete solution to the latter problem in the smooth case (see [69] and [75]).

An important fundamental direction of Prokhorov’s research is the study of complements on algebraic varieties. The main results on this topic are collected in the two papers [11] and [22] on the construction of complements in small dimensions, which were written jointly with V. V. Shokurov. These partial results, in combination with the inductive method itself, were used by Birkar for higher dimensions. The works by Prokhorov and Shokurov also introduced many important concepts, which are now widely used in birational geometry (like Fano-type and Calabi–Yau-type varieties, hyperstandard coefficients, b-semiampleness) and many questions (like the Prokhorov–Shokurov conjecture on the b-semiampleness of the moduli part of the adjunction formula). The applications of the theory of complements to classical results in the theory of algebraic surfaces, such as Kawamata’s classification of log-terminal singularities and Kodaira’s classification of degenerations of elliptic curves, are described in [10].

Another important direction developed by Prokhorov concerns the degenerations of smooth del Pezzo surfaces. On the one hand, in the joint work with Mori [20] they found important restrictions on the degenerations of such surfaces in Mori fibre spaces over a curve; namely, they proved a bound of $6$ for the multiplicity of fibres (which proved a special case of a general conjecture due to Shokurov on the singularities of the base of an lc-trivial fibration) and gave an explicit description of degenerations of multiplicity at least $2$. Soon after that, in a joint work with P. Hacking, Prokhorov [23] found a connection of degenerations of del Pezzo surfaces with Markov triples and, more generally, with triples of positive integer solutions of Diophantine equations of Markov type. These papers form a part of a series of works on degenerations of del Pezzo surfaces, which won him the A. A. Markov Prize. One more paper from this series [39] studies important numerical invariants of the central fibres of degenerations of smooth del Pezzo surfaces; it is proved there that the number of non-Du Val singularities of the central fibre does not exceed the Picard rank of the central fibre plus $2$, and in the case of equality the central fibre is a toric surface. Furthermore, for those degenerations which have terminal singularities, the conjecture of Reid on the existence of an $1$-complement with Du Val singularities is proved.

Together with J. McKernan, Prokhorov [12] showed that accumulation points of log canonical thresholds in dimension $3$ are log-canonical thresholds in dimension $2$, except for the largest threshold, which is equal to $1$. They also checked that a similar result in an arbitrary dimension follows from the Minimal Model Program and the Borisov–Alexeev–Borisov conjecture. Up-to-date techniques let the proof of McKernan and Prokhorov go through in any dimension.

Let us mention a series of joint work of Prokhorov with T. Kishimoto and Zaidenberg, concerning the flexibility of affine cones over Fano varieties, that is, the existence of a large supply of unipotent groups acting on cones. It turns out that the existence of at least one such action on the affine Veronese cone over a polarized Fano variety is equivalent to the existence of a polar cylinder in the variety: see [26] and [31]. They also showed that del Pezzo surfaces of degrees $1$, $2$, and $3$ are not cylindrical, while starting from degree $4$ they admit many cylinders, which proves the flexibility of affine cones over these del Pezzo surfaces. Similar results in dimensions $3$ and $4$ were obtained in [35], [36], [45], [47], and [74]. Subsequently, a large group of researchers joined this project; see the survey [56].

Apart from the directions listed above, Prokhorov has results in some other areas of algebraic geometry. We can mention works on exceptional singularities [6], [7], [9], [8], a simple proof of the non-rationality of a general quartic double solid [46], and a classification of higher-dimensional del Pezzo and almost del Pezzo varieties [68].

Prokhorov’s scientific contributions are widely recognized in Russia and internationally. He is a recipient of the I. I. Shuvalov Prize and A. A. Markov Prize. He was an invited speaker at the European Congress of Mathematics in 2020 and at the International Congress of Mathematicians in 2022. In 2019 he was elected a corresponding member of the Russian Academy of Sciences.

Yuri Prokhorov is not only a distinguished researcher; he also plays a vital role in mathematical education in the field of algebraic geometry. Following the tragic death of V. A. Iskovskikh in 2009, Prokhorov took over the leadership of the Iskovskikh Seminar at the Steklov Mathematical Institute, which continues to be a vibrant centre for young algebraic geometers. He has also led for many years a seminar on algebraic geometry in the Scientific and Educational Center of the Steklov Institute. He maintains a strong connection with the Faculty of Mechanics and Mathematics at Moscow State University, where he reads lectures and teaches advanced courses.

Under his supervision many graduate students defended their Kandidat dissertations, including D. A. Stepanov, C. A. Shramov (who later earned a D.Sc. degree), N. F. Zak, I. V. Karzhemanov, G. N. Belousov, V. I. Tsygankov, A. S. Trepalin, A. A. Avilov, E. A. Yasinsky, and K. V. Loginov. Since the foundation of the Faculty of Mathematics at the HSE University, many students from there have also become Prokhorov’s mentees.

Prokhorov’s books, monographs, surveys, and lecture notes are masterfully written and serve as indispensable references for students beginning to study algebraic geometry and venerable researchers alike. Among them are the book Fano varieties [5] (joint with Iskovskikh), the surveys “The rationality problem for conic bundles” [50] and “Equivariant minimal model program” [59], the lecture notes Elliptic curves and cryptography [15], Singularities of algebraic varieties [21], Rational surfaces [41], and Fano threefolds [62].

In addition to teaching, Prokhorov is deeply involved in scientific administration. For many years, he served on the Expert Council on Mathematics and Mechanics of the Higher Attestation Commission of the Russian Federation, and since 2023 he chairs Dissertation Council 24.1.167.03 at the Steklov Institute. He is also a member of the dissertation council at the Faculty of Mathematics of the HSE University, works on expert panels and prize juries for numerous prestigious awards, and is a member of the editorial boards of several Russian and international mathematics journals.

We wish Yuri Gennadievich Prokhorov continued good health, new successes in tackling fundamental mathematical problems, talented new students — and, of course, personal happiness!

List of cited papers of Yu. G. Prokhorov
1.	I. Ya. Kolpakov-Miroshnichenko and Yu. G. Prokhorov, “Rationality of the field of invariants of a faithful four-dimensional representation of the icosahedral group”, Math. Notes, 41:4 (1987), 270–272
2.	Yu. G. Prokhorov, “Automorphism groups of Fano manifolds”, Russian Math. Surveys, 45:3 (1990), 222–223
3.	I. Ya. Kolpakov-Miroshnichenko and Yu. G. Prokhorov, “Rationality of fields of invariants of some four-dimensional linear groups, and an equivariant construction related to the Segre cubic”, Math. USSR-Sb., 74:1 (1993), 169–183
4.	I. Ya. Kolpakov-Miroshnichenko and Yu. G. Prokhorov, “Rationality construction of fields of invariants of some finite four-dimensional linear groups associated with Fano threefolds”, Math. Notes, 51:1 (1992), 74–76
5.	V. A. Iskovskikh and Yu. G. Prokhorov, “Fano varieties”, Algebraic geometry V, Encyclopaedia Math. Sci., 47, Springer, Berlin, 1999, 1–247
6.	D. G. Markushevich and Yu. G. Prokhorov, “Klein's group defines an exceptional singularity of dimension 3”, Algebraic geometry IX, J. Math. Sci. (N. Y.), 94:1 (1999), 1060–1067
7.	D. Markushevich and Yu. G. Prokhorov, “Exceptional quotient singularities”, Amer. J. Math., 121:6 (1999), 1179–1189
8.	Yu. G. Prokhorov, “Sparseness of exceptional quotient singularities”, Math. Notes, 68:5 (2000), 664–667
9.	Sh. Ishii and Yu. Prokhorov, “Hypersurface exceptional singularities”, Internat. J. Math., 12:6 (2001), 661–687
10.	Yu. G. Prokhorov, Lectures on complements on log surfaces, MSJ Mem., 10, Math. Soc. Japan, Tokyo, 2001, viii+130 pp.
11.	Yu. G. Prokhorov and V. V. Shokurov, “The first main theorem on complements: from global to local”, Izv. Math., 65:6 (2001), 1169–1196
12.	J. McKernan and Yu. Prokhorov, “Threefold thresholds”, Manuscripta Math., 114:3 (2004), 281–304
13.	Yu. G. Prokhorov, “On the degree of Fano threefolds with canonical Gorenstein singularities”, Sb. Math., 196:1 (2005), 77–114
14.	Yu. G. Prokhorov, “The degree of $\mathbb Q$-Fano threefolds”, Sb. Math., 198:11 (2007), 1683–1702
15.	Yu. G. Prokhorov, Elliptic curves and criptography, Semester 1, Faculty of Mechanics and Mathematics of Moscow State University, Moscow, 2007, 144 pp. (Russian)
16.	Huah Chu, Shou-Jen Hu, Ming-chang Kang, and Y. G. Prokhorov, “Noether's problem for groups of order 32”, J. Algebra, 320:7 (2008), 3022–3035
17.	S. Mori and Yu. Prokhorov, “On $\mathbb{Q}$-conic bundles”, Publ. Res. Inst. Math. Sci., 44:2 (2008), 315–369
18.	S. Mori and Yu. Prokhorov, “On $\mathbb{Q}$-conic bundles. II”, Publ. Res. Inst. Math. Sci., 44:3 (2008), 955–971
19.	S. Mori and Yu. Prokhorov, “On $\mathbb{Q}$-conic bundles. III”, Publ. Res. Inst. Math. Sci., 45:3 (2009), 787–810
20.	S. Mori and Yu. G. Prokhorov, “Multiple fibers of del Pezzo fibrations”, Multidimensional algebraic geometry, Tr. Mat. Inst. Steklova, 264, MAIK ‘Nauka/Interperiodika’, Moscow, 2009, 137–151      ; Proc. Steklov Inst. Math., 264 (2009), 131–145
21.	Yu. G. Prokhorov, Singularities of algebraic manifolds, Moscow Center for Continuous Mathematical Education, Moscow, 2009, 128 pp. (Russian)
22.	Yu. G. Prokhorov and V. V. Shokurov, “Towards the second main theorem on complements”, J. Algebraic Geom., 18:1 (2009), 151–199
23.	P. Hacking and Yu. Prokhorov, “Smoothable del Pezzo surfaces with quotient singularities”, Compos. Math., 146:1 (2010), 169–192
24.	Ming-chang Kang and Yu. G. Prokhorov, “Rationality of three-dimensional quotients by monomial actions”, J. Algebra, 324:9 (2010), 2166–2197
25.	Yu. G. Prokhorov, “Fields of invariants of finite linear groups”, Cohomological and geometric approaches to rationality problems, Progr. Math., 282, Birkhäuser Boston, Inc., Boston, MA, 2010, 245–273
26.	T. Kishimoto, Yu. Prokhorov, and M. Zaidenberg, “Group actions on affine cones”, Affine algebraic geometry, CRM Proc. Lecture Notes, 54, Amer. Math. Soc., Providence, RI, 2011, 123–163
27.	S. Mori and Yu. Prokhorov, “Threefold extremal contractions of type (IA)”, Kyoto J. Math., 51:2 (2011), 393–438
28.	Yu. Prokhorov, “$p$-elementary subgroups of the Cremona group of rank 3”, Classification of algebraic varieties, EMS Ser. Congr. Rep., Eur. Math. Soc. (EMS), Zürich, 2011, 327–338
29.	Yu. Prokhorov, “Simple finite subgroups of the Cremona group of rank 3”, J. Algebraic Geom., 21:3 (2012), 563–600
30.	F. Bogomolov and Yu. Prokhorov, “On stable conjugacy of finite subgroups of the plane Cremona group. I”, Cent. Eur. J. Math., 11:12 (2013), 2099–2105
31.	T. Kishimoto, Yu. Prokhorov, and M. Zaidenberg, “$\mathbb{G}_\mathrm a$-actions on affine cones”, Transform. Groups, 18:4 (2013), 1137–1153
32.	Yu. Prokhorov, “$G$-Fano threefolds. I”, Adv. Geom., 13:3 (2013), 389–418
33.	Yu. Prokhorov, “$G$-Fano threefolds. II”, Adv. Geom., 13:3 (2013), 419–434
34.	Yu. G. Prokhorov, “On birational involutions of $\mathbb P^3$”, Izv. Math., 77:3 (2013), 627–648
35.	T. Kishimoto, Yu. Prokhorov, and M. Zaidenberg, “Affine cones over Fano threefolds and additive group actions”, Osaka J. Math., 51:4 (2014), 1093–1112
36.	T. Kishimoto, Yu. Prokhorov, and M. Zaidenberg, “Unipotent group actions on del Pezzo cones”, Algebr. Geom., 1:1 (2014), 46–56
37.	Yu. Prokhorov, “2-elementary subgroups of the space Cremona group”, Automorphisms in birational and affine geometry, Springer Proc. Math. Stat., 79, Springer, Cham, 2014, 215–229
38.	Yu. Prokhorov and C. Shramov, “Jordan property for groups of birational selfmaps”, Compos. Math., 150:12 (2014), 2054–2072
39.	Yu. Prokhorov, “A note on degenerations of del Pezzo surfaces”, Ann. Inst. Fourier (Grenoble), 65:1 (2015), 369–388
40.	Yu. Prokhorov, “On stable conjugacy of finite subgroups of the plane Cremona group. II”, Michigan Math. J., 64:2 (2015), 293–318
41.	Yu. G. Prokhorov, “Rational surfaces”, Lecture Courses of Scientific and educational Centre, 24, Steklov Mathematical Institute, Moscow, 2015, 3–76 (Russian)
42.	S. Mori and Yu. G. Prokhorov, “Threefold extremal contractions of type (IIA). I”, Izv. Math., 80:5 (2016), 884–909
43.	Yu. Prokhorov and M. Reid, “On $\mathbb Q$-Fano 3-folds of Fano index 2”, Minimal models and extremal rays (Kyoto 2011), Adv. Stud. Pure Math., 70, Math. Soc. Japan, Tokyo, 2016, 397–420
44.	Yu. Prokhorov and C. Shramov, “Jordan property for Cremona groups”, Amer. J. Math., 138:2 (2016), 403–418
45.	Yu. Prokhorov and M. Zaidenberg, “Examples of cylindrical Fano fourfolds”, Eur. J. Math., 2:1 (2016), 262–282
46.	Yu. Prokhorov, “A simple proof of the non-rationality of a general quartic double solid”, Bull. Korean Math. Soc., 54:5 (2017), 1619–1625
47.	Yu. Prokhorov and M. Zaidenberg, “New examples of cylindrical Fano fourfolds”, Algebraic varieties and automorphism groups, Adv. Stud. Pure Math., 75, Math. Soc. Japan, Tokyo, 2017, 443–463
48.	A. Kuznetsov and Yu. Prokhorov, “Prime Fano threefolds of genus 12 with a $\mathbb G_{\mathrm m}$-action”, Épijournal Géom. Algébrique, 2 (2018), 3, 14 pp.
49.	A. G. Kuznetsov, Yu. G. Prokhorov, and C. A. Shramov, “Hilbert schemes of lines and conics and automorphism groups of Fano threefolds”, Jpn. J. Math., 13:1 (2018), 109–185
50.	Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456
51.	Yu. Prokhorov and C. Shramov, “Finite groups of birational selfmaps of threefolds”, Math. Res. Lett., 25:3 (2018), 957–972
52.	Yu. Prokhorov and C. Shramov, “$p$-subgroups in the space Cremona group”, Math. Nachr., 291:8-9 (2018), 1374–1389
53.	Yu. Prokhorov and M. Zaidenberg, “Fano–Mukai fourfolds of genus $10$ as compactifications of $\mathbb{C}^4$”, Eur. J. Math., 4:3 (2018), 1197–1263
54.	S. Mori and Yu. G. Prokhorov, “Threefold extremal curve germs with one non-Gorenstein point”, Izv. Math., 83:3 (2019), 565–612
55.	Yu. G. Prokhorov and C. A. Shramov, “Finite groups of bimeromorphic selfmaps of uniruled Kähler threefolds”, Izv. Math., 84:5 (2020), 978–1001
56.	I. Cheltsov, J. Park, Yu. Prokhorov, and M. Zaidenberg, “Cylinders in Fano varieties”, EMS Surv. Math. Sci., 8:1-2 (2021), 39–105
57.	I. Cheltsov and Yu. Prokhorov, “Del Pezzo surfaces with infinite automorphism groups”, Algebr. Geom., 8:3 (2021), 319–357
58.	S. Mori and Yu. G. Prokhorov, “General elephants for threefold extremal contractions with one-dimensional fibres: exceptional case”, Sb. Math., 212:3 (2021), 351–373
59.	Yu. G. Prokhorov, “Equivariant minimal model program”, Russian Math. Surveys, 76:3 (2021), 461–542
60.	Yu. Prokhorov and C. Shramov, “Automorphism groups of compact complex surfaces”, Int. Math. Res. Not. IMRN, 2021:14 (2021), 10490–10520
61.	J. Blanc, I. Cheltsov, A. Duncan, and Yu. Prokhorov, “Birational self-maps of threefolds of (un)-bounded genus or gonality”, Amer. J. Math., 144:2 (2022), 575–597
62.	Yu. G. Prokhorov, “Fano threefolds”, Proc. Steklov Inst. Math., 328, Suppl. 1 (2025), S1–S130
63.	Yu. Prokhorov, “Conic bundle structures on $\mathbb{Q}$-Fano threefolds”, Electron. Res. Arch., 30:5 (2022), 1881–1897
64.	Yu. Prokhorov, “Rationality of $\mathbb{Q}$-Fano threefolds of large Fano index”, Recent developments in algebraic geometry. To Miles Reid for his 70th birthday, London Math. Soc. Lecture Note Ser., 478, Cambridge Univ. Press, Cambridge, 2022, 253–274
65.	Yu. G. Prokhorov and C. A. Shramov, “Finite groups of bimeromorphic self-maps of nonuniruled Kähler threefolds”, Sb. Math., 213:12 (2022), 1695–1714
66.	Yu. Prokhorov and M. Zaidenberg, “Fano–Mukai fourfolds of genus 10 and their automorphism groups”, Eur. J. Math., 8:2 (2022), 561–572
67.	J. Blanc, I. Cheltsov, A. Duncan, and Yu. Prokhorov, “Finite quasisimple groups acting on rationally connected threefolds”, Math. Proc. Cambridge Philos. Soc., 174:3 (2023), 531–568
68.	A. G. Kuznetsov and Yu. G. Prokhorov, “On higher-dimensional del Pezzo varieties”, Izv. Math., 87:3 (2023), 488–561
69.	A. Kuznetsov and Yu. Prokhorov, “Rationality of Fano threefolds over non-closed fields”, Amer. J. Math., 145:2 (2023), 335–411
70.	Yu. Prokhorov, “Embeddings of the symmetric groups to the space Cremona group”, Birational geometry, Kähler–Einstein metrics and degenerations, Springer Proc. Math. Stat., 409, Springer, Cham, 2023, 749–762
71.	Yu. Prokhorov, “Effective results in the three-dimensional minimal model program”, International congress of mathematicians (ICM 2022), Sect. 1–4, v. 3, EMS Press, Berlin, 2023, 2324–2345
72.	Yu. Prokhorov, “Finite groups of birational transformations”, European congress of mathematics, EMS Press, Berlin, 2023, 413–437
73.	Yu. G. Prokhorov and C. A. Shramov, “Jordan property for the Cremona group over a finite field”, Proc. Steklov Inst. Math., 320 (2023), 278–289
74.	Yu. Prokhorov and M. Zaidenberg, “Affine cones over Fano–Mukai fourfolds of genus 10 are flexible”, The art of doing algebraic geometry, Trends Math., Birkhäuser/Springer, Cham, 2023, 363–383
75.	A. Kuznetsov and Yu. Prokhorov, “Rationality over nonclosed fields of Fano threefolds with higher geometric Picard rank”, J. Inst. Math. Jussieu, 23:1 (2024), 207–247
76.	Yu. Prokhorov, “On the birational geometry of $\mathbb{Q}$-Fano threefolds of large Fano index. I”, Ann. Univ. Ferrara Sez. VII Sci. Mat., 70:3 (2024), 955–985

Citation in format AMSBIB

\Bibitem{AleGorZai25}
\by V.~A.~Alexeev, S.~O.~Gorchinskiy, M.~G.~Zaidenberg, A.~G.~Kuznetsov, J.~McKernan, S.~Mori, D.~O.~Orlov, V.~V.~Przyjalkowski, N.~A.~Tyurin, A.~I.~Shafarevich, V.~V.~Shokurov, C.~A.~Shramov
\paper Yurii Gennadievich Prokhorov (on his sixtieth birthday)
\jour Russian Math. Surveys
\yr 2025
\vol 80
\issue 4
\pages 733--741
\mathnet{http://mi.mathnet.ru/eng/rm10253}
\crossref{https://doi.org/10.4213/rm10253e}