Knowledge (XXG)

Peter B. Kronheimer

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422: 1161: 1186: 864: 381: 622: 326: 285: 270: 237:(ALE spaces), leading to the papers "The construction of ALE spaces as hyper-Kähler quotients" and "A Torelli-type theorem for gravitational instantons." He and 78: 1156: 1151: 1166: 1171: 426: 1176: 615: 281: 403:
for knots. They developed an instanton Floer invariant for knots which was used in their proof that Khovanov homology detects the unknot.
384: 595: 847: 766: 388: 1181: 608: 214:, the oldest of the constituent colleges of Oxford University, being an undergraduate, graduate, and full fellow of the college. 632: 519: 586: 1191: 856: 790: 292:'s invariants for 4-manifolds with a distinguished surface. They used the tools developed to prove a conjecture of 1044: 1029: 995: 933: 898: 696: 644: 392: 399:—which had been outstanding for several decades. Another of Kronheimer and Mrowka's results was a proof of the 796: 227: 223: 1141: 923: 840: 61: 550: 491:"A Decade after FAS Moved to Tenure Track, Math Continues on Separate Path | News | The Harvard Crimson" 438: 400: 195: 99: 490: 1146: 1110: 1100: 266: 199: 600: 1120: 1079: 724: 690: 269:(see "Yang-Mills instantons on ALE gravitational instantons.") He was the initial recipient of the 331: 1115: 943: 742: 234: 183: 129: 825: 1049: 1039: 985: 833: 776: 445: 383:. They then went on to develop these tools further and established a structure theorem for 254: 203: 151: 968: 958: 883: 762: 738: 708: 684: 538: 136: 591: 299: 1074: 1024: 810: 718: 678: 515: 407: 396: 289: 238: 71: 1105: 1054: 1034: 948: 918: 913: 903: 888: 800: 772: 702: 434: 411: 246: 211: 207: 141: 1135: 1095: 990: 980: 953: 928: 860: 806: 758: 714: 656: 277: 250: 167: 1000: 893: 734: 672: 662: 262: 171: 85: 543: 1069: 1064: 1059: 938: 908: 780: 748: 666: 293: 119: 650: 415: 258: 230: 179: 175: 92: 1019: 878: 728: 582: 242: 1013: 1006: 974: 17: 814: 786: 577: 465: 562: 444:
Kronheimer's PhD students have included Ian Dowker, Jacob Rasmussen,
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topology. He is William Caspar Graustein Professor of Mathematics at
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Besides his research articles, his writings include a book, with
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their work on embedded surfaces culminated in a proof of the
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Harvard University Department of Mathematics faculty
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Leroy P. Steele Prize for Seminal Contribution 2023
147: 135: 125: 115: 67: 57: 49: 41: 34: 578:Peter Kronheimer's home page at Harvard University 433:. In 2018 he gave a plenary lecture at the ICM in 375: 320: 261:construction. This constructions identified these 1187:International Mathematical Olympiad participants 186:and former chair of the mathematics department. 288:, and their first work developed analogues of 286:Mathematical Research Institute of Oberwolfach 841: 616: 8: 410:, on 4-manifolds, and a book with Mrowka on 276:Kronheimer has frequently collaborated with 273:in 1998 on the basis of some of this work. 848: 834: 826: 623: 609: 601: 31: 542: 365: 333: 301: 427:International Congress of Mathematicians 457: 524:by Peter Kronheimer and Tomasz Mrowka" 441:for Seminal Contribution to Research. 226:, in particular the classification of 282:Massachusetts Institute of Technology 210:. He has had a long association with 7: 284:. Their collaboration began at the 1157:21st-century British mathematicians 1152:20th-century British mathematicians 596:International Mathematical Olympiad 25: 1167:Fellows of Merton College, Oxford 385:Donaldson's polynomial invariants 1172:Alumni of Merton College, Oxford 296:, that the four-ball genus of a 633:Oswald Veblen Prize in Geometry 389:Kronheimer–Mrowka basic classes 245:on ALE spaces generalizing the 222:Kronheimer's early work was on 362: 350: 347: 335: 315: 303: 1: 592:Peter B. Kronheimer's results 587:Mathematics Genealogy Project 544:10.1090/s0273-0979-09-01250-6 531:Bull. Amer. Math. Soc. (N.S.) 522:Monopoles and three-manifolds 412:Seiberg–Witten–Floer homology 265:as moduli spaces for certain 1177:Fellows of the Royal Society 376:{\displaystyle (p-1)(q-1)/2} 45:1963 (age 60–61) 1208: 899:Richard Dickinson Chambers 645:Christos Papakyriakopoulos 448:, and Olga Plamenevskaya. 233:with asymptotical locally 639: 166:(born 1963) is a British 164:Peter Benedict Kronheimer 157: 108: 391:. After the arrival of 224:gravitational instantons 194:Kronheimer attended the 174:and its applications to 170:, known for his work on 1182:Whitehead Prize winners 241:gave a construction of 206:under the direction of 516:Taubes, Clifford Henry 377: 322: 62:Merton College, Oxford 797:Fernando Codá Marques 439:Leroy P. Steele Prize 401:Property P conjecture 393:Seiberg–Witten theory 378: 323: 321:{\displaystyle (p,q)} 196:City of London School 100:Leroy P. Steele Prize 27:British mathematician 1111:Martin David Kruskal 1101:Walter Jakob Gehring 332: 300: 1192:British topologists 1121:Stanley B. Prusiner 964:Peter B. Kronheimer 725:Richard S. Hamilton 691:James Harris Simons 583:Peter B. Kronheimer 198:. He completed his 36:Peter B. Kronheimer 1116:George Andrew Olah 944:Paul Gordon Jarvis 743:Michael J. Hopkins 631:Recipients of the 495:www.thecrimson.com 421:In 1990 he was an 373: 318: 235:Euclidean geometry 184:Harvard University 130:Harvard University 1129: 1128: 1050:Richard E. Taylor 1040:Bernard Silverman 986:Richard G. Morris 823: 822: 777:William Minicozzi 446:Ciprian Manolescu 271:Oberwolfach prize 204:Oxford University 161: 160: 152:Ciprian Manolescu 148:Doctoral students 110:Scientific career 79:Oberwolfach Prize 16:(Redirected from 1199: 975:James R. Maxwell 969:Philippa Marrack 959:Philip Kocienski 884:J. Michael Brady 850: 843: 836: 827: 755:Peter Kronheimer 739:Yakov Eliashberg 709:Michael Freedman 685:William Thurston 625: 618: 611: 602: 565: 560: 554: 548: 546: 528: 512: 506: 505: 503: 501: 487: 481: 480: 478: 476: 462: 382: 380: 379: 374: 369: 327: 325: 324: 319: 137:Doctoral advisor 104: 97: 90: 83: 76: 32: 21: 1207: 1206: 1202: 1201: 1200: 1198: 1197: 1196: 1132: 1131: 1130: 1125: 1084: 1075:Richard D. Wood 1025:Giacinto Scoles 867: 854: 824: 819: 811:Simon Donaldson 719:Clifford Taubes 679:Dennis Sullivan 635: 629: 574: 569: 568: 561: 557: 526: 514: 513: 509: 499: 497: 489: 488: 484: 474: 472: 464: 463: 459: 454: 423:invited speaker 408:Simon Donaldson 397:Thom conjecture 330: 329: 328:-torus knot is 298: 297: 290:Simon Donaldson 239:Hiraku Nakajima 220: 192: 102: 98: 95: 91: 88: 84: 81: 77: 74: 72:Whitehead Prize 58:Alma mater 37: 28: 23: 22: 15: 12: 11: 5: 1205: 1203: 1195: 1194: 1189: 1184: 1179: 1174: 1169: 1164: 1159: 1154: 1149: 1144: 1134: 1133: 1127: 1126: 1124: 1123: 1118: 1113: 1108: 1106:Roy J. Glauber 1103: 1098: 1092: 1090: 1086: 1085: 1083: 1082: 1080:Graham C. Wood 1077: 1072: 1067: 1062: 1057: 1055:Neil Trudinger 1052: 1047: 1042: 1037: 1035:Wilson Sibbett 1032: 1027: 1022: 1017: 1014:Alan Rickinson 1010: 1003: 998: 996:George Pickett 993: 988: 983: 978: 971: 966: 961: 956: 951: 949:Charles K. Kao 946: 941: 936: 931: 926: 921: 919:Richard Fortey 916: 914:Laurence Eaves 911: 906: 904:Colin W. Clark 901: 896: 891: 889:Michael Bulmer 886: 881: 875: 873: 869: 868: 855: 853: 852: 845: 838: 830: 821: 820: 818: 817: 803: 793: 783: 773:Tobias Colding 769: 751: 745: 731: 721: 711: 705: 703:Shing-Tung Yau 699: 697:Mikhail Gromov 693: 687: 681: 675: 669: 659: 653: 647: 640: 637: 636: 630: 628: 627: 620: 613: 605: 599: 598: 589: 580: 573: 572:External links 570: 567: 566: 555: 537:(3): 505–509. 507: 482: 470:54.172.237.215 456: 455: 453: 450: 435:Rio de Janeiro 372: 368: 364: 361: 358: 355: 352: 349: 346: 343: 340: 337: 317: 314: 311: 308: 305: 219: 216: 212:Merton College 208:Michael Atiyah 191: 188: 159: 158: 155: 154: 149: 145: 144: 142:Michael Atiyah 139: 133: 132: 127: 123: 122: 117: 113: 112: 106: 105: 69: 65: 64: 59: 55: 54: 51: 47: 46: 43: 39: 38: 35: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 1204: 1193: 1190: 1188: 1185: 1183: 1180: 1178: 1175: 1173: 1170: 1168: 1165: 1163: 1160: 1158: 1155: 1153: 1150: 1148: 1145: 1143: 1142:Living people 1140: 1139: 1137: 1122: 1119: 1117: 1114: 1112: 1109: 1107: 1104: 1102: 1099: 1097: 1096:Thomas Eisner 1094: 1093: 1091: 1087: 1081: 1078: 1076: 1073: 1071: 1068: 1066: 1063: 1061: 1058: 1056: 1053: 1051: 1048: 1046: 1045:Richard Sykes 1043: 1041: 1038: 1036: 1033: 1031: 1028: 1026: 1023: 1021: 1018: 1016: 1015: 1011: 1009: 1008: 1004: 1002: 999: 997: 994: 992: 991:Chris Perrins 989: 987: 984: 982: 981:Tim Mitchison 979: 977: 976: 972: 970: 967: 965: 962: 960: 957: 955: 954:Barry Keverne 952: 950: 947: 945: 942: 940: 937: 935: 932: 930: 929:Douglas Gough 927: 925: 922: 920: 917: 915: 912: 910: 907: 905: 902: 900: 897: 895: 892: 890: 887: 885: 882: 880: 877: 876: 874: 870: 866: 862: 861:Royal Society 858: 851: 846: 844: 839: 837: 832: 831: 828: 816: 812: 808: 807:Xiuxiong Chen 804: 802: 798: 794: 792: 788: 784: 782: 778: 774: 770: 768: 764: 763:Peter Ozsváth 760: 759:Tomasz Mrowka 756: 752: 750: 746: 744: 740: 736: 732: 730: 726: 722: 720: 716: 715:Andrew Casson 712: 710: 706: 704: 700: 698: 694: 692: 688: 686: 682: 680: 676: 674: 670: 668: 664: 660: 658: 657:Stephen Smale 654: 652: 648: 646: 642: 641: 638: 634: 626: 621: 619: 614: 612: 607: 606: 603: 597: 593: 590: 588: 584: 581: 579: 576: 575: 571: 564: 559: 556: 552: 545: 540: 536: 532: 525: 523: 517: 511: 508: 496: 492: 486: 483: 471: 467: 461: 458: 451: 449: 447: 442: 440: 436: 432: 428: 424: 419: 417: 413: 409: 404: 402: 398: 394: 390: 386: 370: 366: 359: 356: 353: 344: 341: 338: 312: 309: 306: 295: 291: 287: 283: 279: 278:Tomasz Mrowka 274: 272: 268: 264: 263:moduli spaces 260: 256: 252: 248: 244: 240: 236: 232: 229: 225: 217: 215: 213: 209: 205: 201: 197: 189: 187: 185: 181: 180:4-dimensional 177: 173: 169: 168:mathematician 165: 156: 153: 150: 146: 143: 140: 138: 134: 131: 128: 124: 121: 118: 114: 111: 107: 101: 94: 87: 80: 73: 70: 66: 63: 60: 56: 52: 48: 44: 40: 33: 30: 19: 1012: 1007:Kenneth Reid 1005: 1001:George Poste 973: 963: 924:David Garner 894:John Burland 767:Zoltán SzabĂł 754: 735:Jeff Cheeger 673:Robion Kirby 663:Morton Brown 558: 551:"Siebenmann" 534: 530: 521: 510: 498:. Retrieved 494: 485: 473:. Retrieved 469: 460: 443: 420: 418:of the AMS. 405: 275: 221: 193: 172:gauge theory 163: 162: 126:Institutions 109: 86:Veblen Prize 29: 1147:1963 births 1070:Alan Windle 1065:Simon White 1060:Robin Weiss 1030:James Scott 939:Julian Jack 909:David Clary 801:AndrĂ© Neves 791:Daniel Wise 781:Paul Seidel 749:David Gabai 667:Barry Mazur 294:John Milnor 231:4-manifolds 228:hyperkähler 120:Mathematics 50:Nationality 1136:Categories 934:John Hinch 651:Raoul Bott 500:23 October 475:23 October 452:References 416:Doob Prize 243:instantons 93:Doob Prize 18:Kronheimer 1020:Leo Sachs 879:Mike Bate 729:Gang Tian 520:"Review: 429:(ICM) in 357:− 342:− 280:from the 190:Education 863:elected 815:Song Sun 787:Ian Agol 553:occurs.) 518:(2009). 255:Drinfeld 1089:Foreign 872:Fellows 865:in 1997 859:of the 857:Fellows 585:at the 425:at the 267:quivers 251:Hitchin 53:British 387:using 247:Atiyah 218:Career 116:Fields 103:(2023) 96:(2011) 89:(2007) 82:(1998) 75:(1993) 68:Awards 805:2019 795:2016 785:2013 771:2010 753:2007 747:2004 741:and 733:2001 723:1996 713:1991 707:1986 701:1981 695:1981 689:1976 683:1976 677:1971 671:1971 661:1966 655:1966 649:1964 643:1964 527:(PDF) 431:Kyoto 259:Manin 200:DPhil 813:and 799:and 789:and 775:and 765:and 757:and 727:and 717:and 665:and 502:2020 477:2020 178:and 42:Born 594:at 539:doi 202:at 1138:: 809:, 779:; 761:; 737:, 535:46 533:. 529:. 493:. 468:. 176:3- 849:e 842:t 835:v 624:e 617:t 610:v 547:. 541:: 504:. 479:. 371:2 367:/ 363:) 360:1 354:q 351:( 348:) 345:1 339:p 336:( 316:) 313:q 310:, 307:p 304:( 257:– 253:– 249:– 20:)

Index

Kronheimer
Merton College, Oxford
Whitehead Prize
Oberwolfach Prize
Veblen Prize
Doob Prize
Leroy P. Steele Prize
Mathematics
Harvard University
Doctoral advisor
Michael Atiyah
Ciprian Manolescu
mathematician
gauge theory
3-
4-dimensional
Harvard University
City of London School
DPhil
Oxford University
Michael Atiyah
Merton College
gravitational instantons
hyperkähler
4-manifolds
Euclidean geometry
Hiraku Nakajima
instantons
Atiyah
Hitchin

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