diff --git a/build.gradle b/build.gradle
index 90251e0e8fa..ff029ad9870 100644
--- a/build.gradle
+++ b/build.gradle
@@ -67,8 +67,8 @@ configure(allprojects) { project ->
 			dependency "io.reactivex:rxjava:1.3.8"
 			dependency "io.reactivex:rxjava-reactive-streams:1.2.1"
 			dependency "io.reactivex.rxjava2:rxjava:2.2.21"
-			dependency "io.reactivex.rxjava3:rxjava:3.1.1"
-			dependency "io.smallrye.reactive:mutiny:1.1.1"
+			dependency "io.reactivex.rxjava3:rxjava:3.1.3"
+			dependency "io.smallrye.reactive:mutiny:1.2.0"
 			dependency "io.projectreactor.tools:blockhound:1.0.6.RELEASE"
 
 			dependency "com.caucho:hessian:4.0.63"
@@ -128,18 +128,18 @@ configure(allprojects) { project ->
 			dependency "org.webjars:webjars-locator-core:0.48"
 			dependency "org.webjars:underscorejs:1.8.3"
 
-			dependencySet(group: 'org.apache.tomcat', version: '9.0.54') {
+			dependencySet(group: 'org.apache.tomcat', version: '9.0.55') {
 				entry 'tomcat-util'
 				entry('tomcat-websocket') {
 					exclude group: "org.apache.tomcat", name: "tomcat-websocket-api"
 					exclude group: "org.apache.tomcat", name: "tomcat-servlet-api"
 				}
 			}
-			dependencySet(group: 'org.apache.tomcat.embed', version: '9.0.54') {
+			dependencySet(group: 'org.apache.tomcat.embed', version: '9.0.55') {
 				entry 'tomcat-embed-core'
 				entry 'tomcat-embed-websocket'
 			}
-			dependencySet(group: 'io.undertow', version: '2.2.12.Final') {
+			dependencySet(group: 'io.undertow', version: '2.2.13.Final') {
 				entry 'undertow-core'
 				entry('undertow-websockets-jsr') {
 					exclude group: "org.jboss.spec.javax.websocket", name: "jboss-websocket-api_1.1_spec"
@@ -164,7 +164,7 @@ configure(allprojects) { project ->
 			dependency 'org.apache.httpcomponents.core5:httpcore5-reactive:5.1.1'
 			dependency "org.eclipse.jetty:jetty-reactive-httpclient:1.1.9"
 
-			dependency "org.jruby:jruby:9.2.19.0"
+			dependency "org.jruby:jruby:9.2.20.1"
 			dependency "org.python:jython-standalone:2.7.1"
 			dependency "org.mozilla:rhino:1.7.11"
 
@@ -206,10 +206,10 @@ configure(allprojects) { project ->
 			}
 			dependency "io.mockk:mockk:1.12.0"
 
-			dependency("net.sourceforge.htmlunit:htmlunit:2.54.0") {
+			dependency("net.sourceforge.htmlunit:htmlunit:2.55.0") {
 				exclude group: "commons-logging", name: "commons-logging"
 			}
-			dependency("org.seleniumhq.selenium:htmlunit-driver:2.54.0") {
+			dependency("org.seleniumhq.selenium:htmlunit-driver:2.55.0") {
 				exclude group: "commons-logging", name: "commons-logging"
 			}
 			dependency("org.seleniumhq.selenium:selenium-java:3.141.59") {
@@ -237,7 +237,7 @@ configure(allprojects) { project ->
 
 			dependency "com.ibm.websphere:uow:6.0.2.17"
 			dependency "com.jamonapi:jamon:2.82"
-			dependency "joda-time:joda-time:2.10.10"
+			dependency "joda-time:joda-time:2.10.13"
 			dependency "org.eclipse.persistence:org.eclipse.persistence.jpa:2.7.9"
 			dependency "org.javamoney:moneta:1.3"
 
@@ -340,7 +340,7 @@ configure([rootProject] + javaProjects) { project ->
 	}
 
 	checkstyle {
-		toolVersion = "9.0"
+		toolVersion = "9.2"
 		configDirectory.set(rootProject.file("src/checkstyle"))
 	}
 
diff --git a/spring-webflux/src/main/java/org/springframework/web/reactive/socket/server/upgrade/TomcatRequestUpgradeStrategy.java b/spring-webflux/src/main/java/org/springframework/web/reactive/socket/server/upgrade/TomcatRequestUpgradeStrategy.java
index f918410dd5e..1d2c641c9be 100644
--- a/spring-webflux/src/main/java/org/springframework/web/reactive/socket/server/upgrade/TomcatRequestUpgradeStrategy.java
+++ b/spring-webflux/src/main/java/org/springframework/web/reactive/socket/server/upgrade/TomcatRequestUpgradeStrategy.java
@@ -123,6 +123,7 @@ public class TomcatRequestUpgradeStrategy implements RequestUpgradeStrategy {
 	}
 
 
+	@SuppressWarnings("deprecation")  // for old doUpgrade variant in Tomcat 9.0.55
 	@Override
 	public Mono<Void> upgrade(ServerWebExchange exchange, WebSocketHandler handler,
 			@Nullable String subProtocol, Supplier<HandshakeInfo> handshakeInfoFactory){
diff --git a/spring-websocket/src/main/java/org/springframework/web/socket/server/standard/TomcatRequestUpgradeStrategy.java b/spring-websocket/src/main/java/org/springframework/web/socket/server/standard/TomcatRequestUpgradeStrategy.java
index c3c6a191609..4f685ad372b 100644
--- a/spring-websocket/src/main/java/org/springframework/web/socket/server/standard/TomcatRequestUpgradeStrategy.java
+++ b/spring-websocket/src/main/java/org/springframework/web/socket/server/standard/TomcatRequestUpgradeStrategy.java
@@ -1,5 +1,5 @@
 /*
- * Copyright 2002-2017 the original author or authors.
+ * Copyright 2002-2021 the original author or authors.
  *
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
@@ -53,6 +53,7 @@ public class TomcatRequestUpgradeStrategy extends AbstractStandardUpgradeStrateg
 		return new String[] {"13"};
 	}
 
+	@SuppressWarnings("deprecation")  // for old doUpgrade variant in Tomcat 9.0.55
 	@Override
 	public void upgradeInternal(ServerHttpRequest request, ServerHttpResponse response,
 			@Nullable String selectedProtocol, List<Extension> selectedExtensions, Endpoint endpoint)