Caucher Birkar | Academic Influence

Why Is Caucher Birkar Influential?

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According to Wikipedia, Caucher Birkar is an Iranian Kurdish mathematician and a professor at Tsinghua University and University of Cambridge. Birkar is an important contributor to modern birational geometry. In 2010 he received the Leverhulme Prize in mathematics and statistics for his contributions to algebraic geometry, and in 2016, shared the AMS Moore Prize for the article "Existence of minimal models for varieties of log general type". He was awarded the Fields Medal in 2018, "for his proof of boundedness of Fano varieties and contributions to the minimal model program". In his office at the University, Birkar has two photographs of Alexander Grothendieck, his favorite mathematician, who like Birkar, was a refugee and Fields medalist.

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Caucher Birkar's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Papers

Singularities of linear systems and boundedness of Fano varieties (2016) (212)
Anti-pluricanonical systems on Fano varieties (2016) (142)
Existence of log canonical flips and a special LMMP (2011) (130)
Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs (2014) (112)
Higher dimensional algebraic geometry in honour of Professor Yujiro Kawamata's sixtieth birthday (2017) (109)
Existence of flips and minimal models for 3-folds in char p (2013) (103)
On existence of log minimal models (2007) (72)
Existence of Mori fibre spaces for 3-folds in char $p$ (2014) (70)
Ascending chain condition for log canonical thresholds and termination of log flips (2007) (68)
On existence of log minimal models II (2009) (66)
Singularities on the base of a Fano type fibration (2012) (39)
On existence of log minimal models and weak Zariski decompositions (2009) (37)
The augmented base locus of real divisors over arbitrary fields (2013) (31)
Polarized pairs, log minimal models, and Zariski decompositions (2014) (28)
The Iitaka conjecture Cn,m in dimension six (2008) (27)
Mld's vs thresholds and flips (2006) (27)
Varieties fibred over abelian varieties with fibres of log general type (2013) (23)
Generalised pairs in birational geometry (2020) (21)
Log Calabi-Yau fibrations (2018) (20)
On connectedness of non-klt loci of singularities of pairs (2020) (19)
Geometry and moduli of polarised varieties (2020) (18)
Log canonical pairs with good augmented base loci (2013) (18)
Minimal models, flips and finite generation : a tribute to V.V. SHOKUROV and Y.-T. SIU (2009) (16)
Boundedness of elliptic Calabi-Yau varieties with a rational section. (2020) (15)
IITAKA $C_{n,m}$ CONJECTURE FOR 3-FOLDS OVER FINITE FIELDS (2015) (13)
Topics in algebraic geometry (2011) (11)
IITAKA’S Cn,m CONJECTURE FOR 3-FOLDS OVER FINITE FIELDS (2015) (10)
Images of manifolds with semi-ample anti-canonical divisor (2016) (10)
Boundedness and volume of generalised pairs (2021) (8)
Algebraic Geometry Lecture Notes (2010) (7)
Log minimal models according to Shokurov (2008) (6)
Boundedness of ̄-Log Canonical Complements on Surfaces (2006) (6)
Supplement to the paper (2011) (6)
On log minimal models and Zariski decompositions II (2013) (5)
ACC for log canonical thresholds and termination of log flips (2005) (5)
On termination of log flips in dimension four (2008) (4)
Singularities on toric fibrations (2020) (4)
On the moduli part of the Kawamata-Kodaira canonical bundle formula (2012) (4)
Divisorial algebras and modules on schemes (2011) (3)
LOG CANONICAL ALGEBRAS AND MODULES (2013) (3)
BIRATIONAL GEOMETRY OF ALGEBRAIC VARIETIES (2017) (2)
Lectures on birational geometry (2012) (2)
Topics in algebraic geometry Lecture notes of an advanced graduate course (2010) (2)
Geometry of polarised varieties (2020) (2)
Variations of generalised pairs (2022) (2)
Boundedness of Fano type fibrations (2022) (1)
Bounding non-rationality of divisors on 3-fold Fano fibrations (2020) (1)
Elements of Nonstandard Algebraic Geometry (2003) (1)
IITAKA Cn,m CONJECTURE FOR 3-FOLDS OVER FINITE FIELDS (2018) (1)
Supplement to the paper "On existence of log minimal models II" (2011) (1)
ABSTRACTS OF LECTURES MODULI 2007 (2007) (0)
Birational geometry (2007) (0)
Algebraic Geometry (2012) (0)
Vyacheslav Vladimirovich Shokurov (2021) (0)
Existence of log canonical flips and a special LMMP (2012) (0)
Anticanonical volume of Fano 4-folds (2022) (0)
Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs (2016) (0)
Part II — Galois Theory (2018) (0)
On existence of log minimal models and weak Zariski decompositions (2011) (0)
Abstracts of Lectures Moduli 2007 September 3 -7, Hokkaido University (2007) (0)
On Shokurov's Log Flips: The 3 dimensional case (2003) (0)
Se p 20 06 Mld ’ s vs thresholds and flips (2008) (0)
ICMS Workshop on Birational Geometry held in honour of Vyacheslav V. Shokurov's 60th birthday (2014) (0)
Boundedness of $\epsilon$-log Canonical Complements on Surfaces (2004) (0)
Moduli of algebraic varieties (2022) (0)
From fields to Fields (2020) (0)
The augmented base locus of real divisors over arbitrary fields (2016) (0)
A Personal Journey into the World of Mathematics (2020) (0)
Boundedness of ǫ-lc Complements on Surfaces (2008) (0)

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